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ASME Conference Presenter Attendance Policy and Archival Proceedings

2011;():i. doi:10.1115/DETC2011-NS4.
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This online compilation of papers from the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2011) represents the archival version of the Conference Proceedings. According to ASME’s conference presenter attendance policy, if a paper is not presented at the Conference, the paper will not be published in the official archival Proceedings, which are registered with the Library of Congress and are submitted for abstracting and indexing. The paper also will not be published in the ASME Digital Library and may not be cited as a published paper.

Commentary by Dr. Valentin Fuster

8th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

2011;():3-11. doi:10.1115/DETC2011-47143.

Variational integrators are developed for dissipative systems with one degree of freedom. The dissipation considered herein is of simple Rayleigh dissipation type. The present formulation is based not on the Lagrange-d’Alembert principle, but on Hamilton’s principle. A benefit for using variational integration techniques is stressed in this paper. The discrete algorithms are obtained by a stationary condition of action integral, in which the Lagrangian is directly discretized. Unlike the existing algorithms, a coupling term between mass and dissipation exists in the present algorithms. A mixed method, in which a velocity is independent on a position coordinate, is presented for dissipative systems. In order to investigate an accuracy of numerical integrators, we introduce a new parameter in addition to the energy decay. Numerical examples show that the present variational, integrators are available for not only highly but also weakly dissipative systems.

Commentary by Dr. Valentin Fuster
2011;():13-22. doi:10.1115/DETC2011-47224.

A general methodology for the dynamic modeling and analysis of planar multibody systems with multiple clearance joints is presented. The inter-connecting body components that constitute a real joint are modeled as colliding bodies, which dynamic behaviors are influenced by geometric, physical and mechanical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory, together with a dissipative term, is used to evaluate the intra-joint contact forces. The incorporation of the friction, based on the classical Coulomb’s friction law, is also included. The suitable contact force models are embedded into the dynamic equations of motion for the multibody system. A simple mechanical system with multiple clearance joints is used to demonstrate the accuracy and efficiency of the presented approach and to discuss the main assumptions and procedures adopted. The effects of single versus multiple clearance joints are discussed.

Commentary by Dr. Valentin Fuster
2011;():23-28. doi:10.1115/DETC2011-47297.

The theory of non-smooth multibody dynamics with unilateral contacts is now well established, for example in terms of measure equations of motion added by complementarities or formulated with the help of differential inclusions. Most researchers today focus on numerical methods for solving these systems, because computing times especially for large systems are a problem. Time-stepping schemes for time-integration, pivoting or iterative algorithms for solving the complementarity problem and the Augmented Lagrangian approach are methods of increasing numerical efficiency for large systems. The paper describes new findings for unilateral multibody systems and discusses two large industrial examples, namely the dynamics of a roller coaster and the behavior of a drop tower featuring hydraulic components.

Commentary by Dr. Valentin Fuster
2011;():29-39. doi:10.1115/DETC2011-47306.

Complex aeroservoelastic and mechatronic systems imply interaction between multidisciplinary or multifield subcomponents, whose dynamics are characterized by problem- and field-specific time scales and frequency ranges. As opposed to what is usually termed monolithic approach to the simulation of coupled problems, where a single formulation (and software solver) directly models the entire problems, the co-simulation approach allows to exploit state-of-art formulations for specific fields by coupling them as appropriate to establish the required interaction between the subcomponents. The interaction problem between the different and even incompatible interfaces of subcomponent domains can be split in spatial and temporal. This work focuses on the latter aspect. In fact, when subdomains require different time scales to achieve the desired trade-off between accuracy and computational cost, multirate methods can be used to avoid the need of a subdomain solver to comply with excessively stringent requirements resulting from another one. Many multirate methods are designed for monoblock systems and used in single-disciplinary simulations (e.g. electric networks). Their application to co-simulation setups may be not straightforward. A key problem in co-simulation, especially when stability and free response of a system are addressed, as in aeroservoelasticity, is related to the numerical stability of the coupled solution process. This work investigates the linear stability properties of a multirate formulation called ‘Double Extrapolation’ (DE) consisting in integrating each subproblem using second-order accurate, L-stable Backward Difference Formulas (BDF) while each subdomain extrapolates the behavior of the other one. It has been chosen because it allows to eliminate most of the idle time of each subdomain solver. The resulting performance gains are illustrated by applying the proposed method to the simulation of a complex aeroservoelastic system consisting in the aeroelastic model of a Horizontal Axis Wind Turbine (HAWT), developed using the general-purpose multibody formulation implemented in the free solver MBDyn, and a dynamic model of the electric generator, modeled in the free general-purpose block-diagram simulation environment ScicosLab. Both modeling environments are real-time capable; thus the proposed system represents an affordable and versatile solution for the hardware-in-the-loop analysis and design of complex multidisciplinary systems.

Commentary by Dr. Valentin Fuster
2011;():41-49. doi:10.1115/DETC2011-47365.

The basis for any model-based control of dynamical systems is an efficient formulation of the motion equations. These are preferably expressed in terms of independent coordinates. In other words the coordinates of a constrained system are split into a set of dependent and independent ones. It is well-known that such coordinate partitioning is not globally valid. A remedy is to switch between different possible sets of minimal coordinates. This drastically increases the numerical complexity and implementation effort, however. In this paper a formulation of the motion equations in redundant coordinates is presented for general non-holonomic systems. This gives rise to a redundant system of differential equations. The formulation is valid in any regular configuration. Because of the singular mass matrix it is not directly applicable for solving the forward dynamics but is tailored for solving the inverse dynamics. An inverse dynamics solution is presented for general full-actuated systems.

Commentary by Dr. Valentin Fuster
2011;():51-58. doi:10.1115/DETC2011-47441.

We analyse a continuous Cosserat model of a visco-elastic rod subjected to a combination of a conservative load and a follower term in one of the ends. The formalism takes into account the geometric non linearities that appear for large deformations from the straight solution. The resulting equation is a PDE whose solution can be analysed for special cases and the eigenvalues of the linearisation can be computed by a combination of numerical continuation and bifurcation results. We illustrate this method analysing the bifurcations of the straight solution of a rod subjected to a follower force. The dynamics and the bifurcation behaviour of the model are explored as the intensity of force is varied and as the mixture of conservative-follower terms varies continuously from the standard conservative case to the purely follower one. Special attention is paid to the corresponding transition from symmetry breaking pitchfork bifurcation (falling over mode) to the appearance of oscillations in a Hopf like bifurcation (if some material damping is included) or pure reversible Hamiltonian Hopf bifurcation in the absence of damping. After the onset of oscillations a complex dynamical behaviour frequently called flutter instability appears. The study is supplemented with the bifurcation analysis of the two elastically jointed follower pendula model as a simplified model of the continuous problem.

Commentary by Dr. Valentin Fuster
2011;():59-66. doi:10.1115/DETC2011-47788.

This paper proposes an explicit-implicit numerical integration method in order to apply to multibody vehicle dynamics model based on a subsystem synthesis method. The subsystem synthesis method can provide effective means to independently analyze each subsystem with virtual reference body. In the proposed method, the explicit integration is used for solving the equations of motion for a base body, while the implicit integration is utilized for obtaining the solutions of the equations of motion for each subsystem. For the purpose of the application of the implicit formulas easily, a subsystem synthesis method with the Cartesian coordinates is developed. In order to show the application viability and effectiveness of the proposed method, an extensive comparative study has been performed through simulations. Then, the proposed method is compared to conventional implicit integration method applied to an overall system. When simulating the bump run of a multibody vehicle model with compliance effect such as bushing elements, the proposed method achieves about 2 times computational speed-up. Furthermore, the simulation study reveals that the larger the number of the attached subsystems is, the better the computational efficiency of the proposed method is than that of the conventional implicit integration method.

Commentary by Dr. Valentin Fuster
2011;():67-76. doi:10.1115/DETC2011-47827.

Efficient dynamics simulations of complex multibody systems are essential in many areas of computer aided engineering and design. As parallel computing resources has become more available, researchers began to reformulate existing algorithms or to create new parallel formulations. Recent works on dynamics simulation of multibody systems include sequential recursive algorithms as well as low order, exact or iterative parallel algorithms. The first part of the paper presents an optimal order parallel algorithm for dynamics simulation of open loop chain multibody systems. The proposed method adopts a Featherstone’s divide and conquer scheme by using Lagrange multipliers approach for constraint imposition and dependent set of coordinates for the system state description. In the second part of the paper we investigate parallel efficiency measures of the proposed formulation. The performance comparisons are made on the basis of theoretical floating-point operations count. The main part of the paper is concetrated on experimental investigation performed on parallel computer using OpenMP threads. Numerical experiments confirm good overall efficiency of the formulation in case of modest parallel computing resources available and demonstrate certain computational advantages over sequential versions.

Commentary by Dr. Valentin Fuster
2011;():77-84. doi:10.1115/DETC2011-47907.

In the work presented in this paper we introduce a novel approach for reducing nonlinear models of mechanical systems organized in an open kinematic chain topology. Starting from the Equation of Motion (EoM) of a constrained mechanical system including different sources of non-linearities, and assuming that the location and type of the non-linear behavior is known, a state space realization is obtained through linearization and standard matricial computation. Hints to generate this distinction are here given and basis towards a general procedure are suggested. Singular perturbation is hence adopted to purge the non-linearly behaving states and to reduce the model’s configuration parameters. The nonlinear portion is maintained in the MB environment, finally linked in a coupled simulation with the reduced first order system.

Commentary by Dr. Valentin Fuster
2011;():85-94. doi:10.1115/DETC2011-48132.

This paper studies the formulation of the dynamics of multibody systems with large rotation variables and kinematic constraints as differential-algebraic equations on a matrix Lie group. Those equations can then be solved using a Lie group time integration method proposed in a previous work. The general structure of the equations of motion are derived from Hamilton principle in a general and unifying framework. Then, in the case of rigid body dynamics, two particular formulations are developed and compared from the viewpoint of the structure of the equations of motion, of the accuracy of the numerical solution obtained by time integration, and of the computational cost of the iteration matrix involved in the Newton iterations at each time step. In the first formulation, the equations of motion are described on a Lie group defined as the Cartesian product of the group of translations R 3 (the Euclidean space) and the group of rotations SO(3 ) (the special group of 3 by 3 proper orthogonal transformations). In the second formulation, the equations of motion are described on the group of Euclidean transformations SE(3 ) (the group of 4 by 4 homogeneous transformations). Both formulations lead to a second-order accurate numerical solution. For an academic example, we show that the formulation on SE(3 ) offers the advantage of an almost constant iteration matrix.

Commentary by Dr. Valentin Fuster
2011;():95-104. doi:10.1115/DETC2011-48144.

When redundant constraints are present in a rigid body mechanism, only selected joint reactions can be determined uniquely, whereas the other cannot. Analytic criteria and numerical methods of finding joints with uniquely solvable reactions are available. In this paper the problem of joint reactions solvability is examined from the point of view of numerical methods frequently used for redundant constrains handling in practical simulations. Three methods are discussed: elimination of redundant constraints, pseudoinverse-based calculations and the augmented Lagrangian method. In each method the redundant constraints are treated differently which — in case of joints with non-unique reactions — leads to different reaction solutions. Moreover, it is shown that one and the same method may lead to different solutions, provided that input data are prepared differently. Finally, it is illustrated that — in case of joints with solvable reactions — the obtained solutions are unique, regardless of the method used for redundant constraints handling.

Commentary by Dr. Valentin Fuster
2011;():105-113. doi:10.1115/DETC2011-48150.

The governing equations for multibody systems are, in general, formulated in the form of differential algebraic equations (DAEs) involving the Lagrange multipliers. It is desirable for efficient and accurate analysis to eliminate the Lagrange multipliers and dependent variables. As a method to solve the DAEs by eliminating the Lagrange multipliers, there is a method called the null space method. In this report, first, it is shown that using the null space matrix one can eliminate the Lagrange multipliers and reduce the number of velocities to that of the independent ones. Then, a new method to obtain the continuous null space matrix is presented. Finally, the presented method is applied to four-bar linkages.

Commentary by Dr. Valentin Fuster
2011;():115-124. doi:10.1115/DETC2011-48366.

According to a recent paper by Laulusa and Bauchau [1], Maggi’s formulation is a simple and stable way to solve the dynamic equations of constrained multibody systems. Among the difficulties of Maggi’s formulation, Laulusa and Bauchau quoted the need for an appropriate choice (and change, when necessary) of independent coordinates, as well as the high cost of computing and updating the basis of the tangent null space of constraint equations. In this paper, index-1 Lagrange’s equations are first considered, including the not-so-rare case of having a singular mass matrix and redundant constraints. The existence and uniqueness of solution for acceleration vector and Lagrange multipliers vector is studied in a very simple way. Then, following Von Schwerin [2], Maggi’s formulation is described as the most efficient way (globally speaking) to solve these index-1 equations. Next, an improved double-step method, which implements the matrix transformations of Maggi’s formulation in an efficient way, is described. Finally, two large real-life examples are presented.

Topics: Equations
Commentary by Dr. Valentin Fuster
2011;():125-135. doi:10.1115/DETC2011-48376.

In molecular simulations, the dominant portion of the computational cost is associated with force field calculations. Herein, we extend the approach used to approximate long range gravitational force and the associated moment in spacecraft dynamics to the coulomb forces present in coarse grained biopolymer simulations. We approximate the resultant force and moment for long-range particle-body and body-body interactions due to the electrostatic force field. The resultant moment approximated here is due to the fact that the net force does not necessarily act through the center of mass of the body (pseudoatom). This moment is considered in multibody-based coarse grain simulations while neglected in bead models which use particle dynamics to address the dynamics of the system. A novel binary divide and conquer algorithm (BDCA) is presented to implement the force field approximation. The proposed algorithm is implemented by considering each rigid/flexible domain as a node of the leaf level of the binary tree. This substructuring strategy is well suited to coarse grain simulations of chain biopolymers using an articulated multibody approach.

Commentary by Dr. Valentin Fuster
2011;():137-146. doi:10.1115/DETC2011-48886.

This paper presents a new methodology for modeling discontinuous dynamics of flexible and rigid multibody systems based on the impulse momentum formulation. The new methodology is based on the seminal idea of the divide and conquer scheme for modeling the forward dynamics of rigid multibody systems. While a similar impulse momentum approach has been demonstrated for multibody systems in tree topologies, this paper presents the generalization of the approach to systems in generalized topologies including many coupled kinematically closed loops. The approach utilizes a hierarchic assembly-disassembly process by traversing the system topology in a binary tree map to solve for the jumps in the system generalized speeds and the constraint impulsive loads in linear and logarithmic cost in serial and parallel implementations, respectively. The coupling between the unilateral and bilateral constraints is handled efficiently through the use of kinematic joint definitions. The generalized impulse momenta equations of flexible bodies are derived using a projection method.

Commentary by Dr. Valentin Fuster
2011;():147-156. doi:10.1115/DETC2011-47081.

The main purpose of this work is to present a general and comprehensive approach to automatically adjust the time step for the contact and non contact periods in multibody dynamics. The basic idea of the described methodology is to ensure that the first impact within a multibody system does not occur with a large value for relative bodies’ penetration in order to avoid the artificially large contact forces associated. The detection of the instant of contact takes place when the distance between two bodies change the sign between two discrete moments in time. In fact, in theory, the contact starts when this distance is zero, or a very small value to prevent the round-off errors. Thus, during the numerical solution of the system equations of motion if the first penetration is below this small value previously specified, then the current time is taken as the impact time. On the other hand, if the first penetration is larger than the specified tolerance, then the current time step is beyond the impact time. In this case, integration algorithm is forced to go back and take a smaller time step until a step can be taken within the acceptable tolerance. The main features of this approach are the easiness to implement and the good computational efficiency. In addition, it can easily deal with the transitions between non contact and contact cases in multibody dynamics. Finally, results obtained from dynamic simulations are presented and discussed to study the validity of the methodology proposed in this work.

Commentary by Dr. Valentin Fuster
2011;():157-166. doi:10.1115/DETC2011-47086.

A general and comprehensive analysis on the continuous contact force models in multibody dynamics is presented and a novel contact force model is proposed. The force models are developed based on the foundation of the Hertz law together with a hysteresis damping parameter that accounts for the energy dissipation during the contact process. In a simple way, these contact force models are based on the analysis and development of three main issues: (i) the dissipated energy associated with the coefficient of restitution that includes the balance of kinetic energy and the conservation of the linear momentum between the initial and final instant of contact; (ii) the stored elastic energy, representing part of initial kinetic energy, which is evaluated as the work done by the contact force developed during the contact process; (iii) the dissipated energy due to internal damping, which is evaluated by modeling the contact process as a single degree-of-freedom system to obtain a hysteresis damping factor. This factor takes into account the geometrical and material properties, as well as the kinematic characteristics of the contacting bodies. The proposed contact force model has the great merit that can be used for contact problems involving materials with low or moderate values of coefficient of restitution. This contact force model is suitable to be included into the equations of motion of a multibody system and contributes to their stable numerical resolution. Two demonstrative examples of application are used to provide the results that support the analysis and discussion of procedures and methodologies adopted in this work.

Commentary by Dr. Valentin Fuster
2011;():167-175. doi:10.1115/DETC2011-47149.

Finite element models can accurately simulate impact-contact dynamics response of a multibody dynamical system. However, such a simulation remains very inefficient because very small integration time step must be used when solving the involved differential equations. Although many model reduction techniques can be used to improve the efficiency of finite element based simulations, most of these techniques cannot be readily applied to contact dynamics simulations due to the high nonlinearity of the contact dynamics model. This paper presents a model reduction approach for finite-element based multibody contact dynamics simulation, based on a modified Lyapunov balanced truncation method. An example is presented to demonstrate that, by applying the model reduction the simulation process is significantly speeded up and the resulting error is bounded within an acceptable level. The performance of the method with respect to some influential factors such as element size, shape and contact stiffness is also investigated.

Commentary by Dr. Valentin Fuster
2011;():177-185. doi:10.1115/DETC2011-47257.

The goal of this work is to study the influence of the contact force model and contact material properties on the dynamic response of a human knee joint. For this purpose, a multibody knee model composed by two rigid bodies, the femur and the tibia, and four nonlinear spring elements that represent the main knee ligaments, is considered. The contact geometrical profiles are extracted from medical images and fitted using spline functions. The tibia motions are modeled, not using a conventional kinematic joint, but rather in terms of the action of the ligaments and potential contact between the bones. Besides, an external force is applied on the center of mass of the tibia in order to simulate the force of the quadriceps muscle group. When a contact is detected, a continuous contact force law is applied. The contact force laws studied are the Hertz, the Hunt-Crossley and the Lankarani-Nikravesh models. Results obtained from computational simulations show that Hertz law is less suitable to describe the dynamic response of the cartilage contact, because this pure elastic model does not account for the viscoelastic nature of the human articulations. Moreover, the effect of the amplitude of the external applied force on the dynamic response of the knee joint model is also evaluated. The obtained results show that the increase of the amplitude of the external applied force increases the contact indentations and lead to an earlier first impact. As far as to the influence of the material contact properties is concerned, the dynamic response of a healthy and natural knee is analyzed and compared with three pathological and two artificial knee models. Results demonstrate that the presence of the cartilage reduces significantly the knee contact forces.

Commentary by Dr. Valentin Fuster
2011;():187-196. doi:10.1115/DETC2011-47360.

Advances in the application of multi-body simulation technology to real world problems have led to an ever increasing demand for higher fidelity modeling techniques. Of these, accurate modeling of friction is of strategic interest in applications such as control system design, automotive suspension analysis, robotics etc. Joints (sometimes referred to as constraints) play an important role in defining the dynamics of a multi-body system. Hence, it is imperative to accurately account for friction forces arising at these joints due to the underlying interface dynamics. In this paper, we discuss the application of LuGre, a dynamic friction model to simulate joint friction. We choose the LuGre model due to its ability to capture important effects such as the Stribeck effect and the Dahl effect. The native 1-d LuGre model is extended to formulate friction computations for non-trivial joint geometries and dynamics in 2 and 3 dimensions. It is also extended to work in the quasi-static regime. Specific applications to revolute, cylindrical and spherical joints in multi-body systems are discussed. Finally, an engineering case study on the effects of joint friction in automotive suspension analysis is presented.

Topics: Friction
Commentary by Dr. Valentin Fuster
2011;():197-205. doi:10.1115/DETC2011-47523.

The problem of two blades with a friction element is studied in order to analyze the effects of the friction on the undesirable vibration suppression. The simplified contact model between friction planes of the blade shrouding and the friction element is derived to be a fast computational tool comparing with a time-consuming finite element solution. The harmonic balance method is suitable for the linearization of originally nonlinear equations of motion under certain assumptions given on the excitation of the system and on its dynamic response. On the other hand the nonlinear equations of motion can be solved directly by their numerical integration, which is more time-consuming but it is not limited by given assumptions. The comparison of results of the harmonic balance method and of the numerical integration of motion equations is given in the paper.

Commentary by Dr. Valentin Fuster
2011;():207-215. doi:10.1115/DETC2011-47709.

The principal aim of this paper is to deal with friction-induced self-excited vibrations in the context of Stribeck law for friction coefficient. More precisely, the theoretical dynamic system under study consists of a single-degree-of-freedom mass-spring-damper oscillator subjected to a velocity-dependent frictional force as it slides on a conveyor belt, following a Stribeck law. We have analyzed the local stability of the static equilibrium and described the created periodic cycle using the averaging method. Numerical continuation with Matcont software is also used for qualitative analysis of this non linear system. In order to validate the theoretical analysis, an original experimental device, the named Lug test rig developed in our laboratory, was employed. For a glass/elastomer contact lubricated with water, friction force and dynamic displacement have been measured. The appearance of the instabilities is explained in relation to the friction measurements.

Topics: Friction , Vibration
Commentary by Dr. Valentin Fuster
2011;():217-226. doi:10.1115/DETC2011-48218.

This study analyses a dynamic multibody model of a deep groove single row ball bearing. The objective of the study is to simulate the dynamic behavior of a bearing under different operational conditions. Typical vibration signals used in bearing diagnostics are simulated using the non-linear Hertzian contact theory. Geometry, material properties, friction and damping coefficients are considered as input while displacements, velocities, accelerations and forces between bearing rings are calculated and validated with the analytical formulations found in literature. Furthermore localized faults are introduced in the simulation in order to extract bearing defect frequencies and to represent the real vibration signal signature in case of fault components. For this purpose, a simplified model is realized using the polygonal contact model. This approach allows to investigate more in detail the effect of localized defects by reproducing the real rolling elements trajectories through a discretization of the contact surfaces. The low computation efficiency compared to the traditional Hertzian approach limits the application of this contact algorithm on the complete bearing model. Nevertheless, the simplified model allows to draw conclusions regarding the influence of the shaft/cage speed on the fault size estimation giving an innovative contribution on bearing diagnostics.

Commentary by Dr. Valentin Fuster
2011;():227-236. doi:10.1115/DETC2011-48347.

This paper describes a software infrastructure made up of tools and libraries designed to assist developers in implementing computational dynamics applications running on heterogeneous and distributed computing environments. Together, these tools and libraries compose a so called Heterogeneous Computing Template (HCT). The heterogeneous and distributed computing hardware infrastructure is assumed herein to be made up of a combination of CPUs and GPUs. The computational dynamics applications targeted to execute on such a hardware topology include many-body dynamics, smoothed-particle hydrodynamics (SPH) fluid simulation, and fluid-solid interaction analysis. The underlying theme of the solution approach embraced by HCT is that of partitioning the domain of interest into a number of sub-domains that are each managed by a separate core/accelerator (CPU/GPU) pair. Five components at the core of HCT enable the envisioned distributed computing approach to large-scale dynamical system simulation: (a) a method for the geometric domain decomposition and mapping onto heterogeneous hardware; (b) methods for proximity computation or collision detection; (c) support for moving data among the corresponding hardware as elements move from subdomain to subdomain; (d) numerical methods for solving the specific dynamics problem of interest; and (e) tools for performing visualization and post-processing in a distributed manner. In this contribution the components (a) and (c) of the HCT are demonstrated via the example of the Discrete Element Method (DEM) for rigid body dynamics with friction and contact. The collision detection task required in frictional-contact dynamics; i.e., task (b) above, is discussed separately and in the context of GPU computing. This task is shown to benefit of a two order of magnitude gain in efficiency when compared to traditional sequential implementations. Note: Reference herein to any specific commercial products, process, or service by trade name, trademark, manufacturer, or otherwise, does not imply its endorsement, recommendation, or favoring by the US Army. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Army, and shall not be used for advertising or product endorsement purposes.

Commentary by Dr. Valentin Fuster
2011;():237-246. doi:10.1115/DETC2011-48405.

This paper presents the solution of the impact problem for a sliding/bouncing baton on flat and inclined planes subject to surface friction. The baton is assumed to have unilaterally constrained motion, which means one end slides on the ground while the other end collides with the ground. We use the impulse momentum approach and incorporate the impulse correlation ratio (ICR) hypothesis to solve the ground impact problem when the system has unilaterally constrained dynamics. Parametric investigations were carried out to examine the effect of the baton’s length and the inclined wall slope angle on the impulse correlation ratio. Numerical simulation and experiments were carried out to validate the model.

Commentary by Dr. Valentin Fuster
2011;():247-255. doi:10.1115/DETC2011-48526.

The use of micro-scale metallic pins in small engineering devices poses numerous problems due to their physical size and the dominant forces which act on micro-scale objects. Assembly and handling of devices with micro-scale parts is problematic because the components are below the threshold of practical, unaided human manipulation and most robotic manipulation. Previous experimental work has shown that applying forced vibrations to unsorted batches of micro-scale objects can order and singulate the objects or produce assemblies of several parts. Planar rigid-body dynamic simulations, which have been previously developed, lack the accuracy necessary for a-priori prediction of the performance of these processes. This paper presents a spatial simulation, based on an impulse-momentum rigid-body model, which more accurately predicts the behavior of micro-pins in a vibratory feeder bowl. The validity of the spatial simulation is verified by improved agreement with previously obtained experimental data.

Commentary by Dr. Valentin Fuster
2011;():257-265. doi:10.1115/DETC2011-48794.

A time-accurate multibody dynamics model for predicting the transient response of toroidal traction drives is presented. The model can be used to predict the system’s transient response due to variations in the input speed, variations in the output load, and changing the speed ratio. The model supports half and full-toroidal configurations, multiple transmitters and multiple cavities. The multibody system representing the toroidal drive is modeled using rigid bodies, revolute joints and rotational actuators. A penalty model is used to impose the joint/contact constraints. The contact model detects contact between discrete points on the surface of the transmitter and an analytical surface representation of the input and output shafts’ toroidal surfaces. A recursive bounding sphere contact search algorithm is used to allow fast contact detection. An elasto-hydrodynamic lubrication model is used for the tangential contact traction forces between the transmitter and the toroid. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The model is partially validated by comparing to previously published steady-state models. The model can help improve the design of toroidal continuous-variable transmission systems including increasing the torque capacity and durability.

Commentary by Dr. Valentin Fuster
2011;():267-273. doi:10.1115/DETC2011-48925.

Impact problems arise in many practical applications. The need of obtaining an accurate model for the inelastic impact is a challenging problem. In general, two approaches are common in solving the impact problems: the impulse-momentum and the compliance based methods. The former approach included the coefficient of restitution which provides a mechanism to solve the problem explicitly. While the compliance methods are generally tailored to solve elastic problems, researchers in the field have proposed several mechanisms to include inelastic losses. In this paper, we present a correlation between the coefficient of restitution in the impulse-momentum based method and the contact stiffness in the compliance methods. We conducted numerical analysis to show that the resulting solutions are indeed identical for a wide range of impact conditions. The numerical results showed that, the two methods can produce similar outcomes if they satisfied a set of end conditions.

Commentary by Dr. Valentin Fuster
2011;():275-284. doi:10.1115/DETC2011-49016.

A volumetric contact dynamics model has been proposed for the purpose of generating reliable and rapid simulations of contact dynamics. Forces and moments between bodies in contact can be expressed in terms of the volume of interference between the undeformed geometries. This allows for the modelling of contact between complex geometries and relatively large contact surfaces, while being computationally less expensive than finite element methods. However, the volumetric model requires experimental validation. Models for simple geometries in contact have been developed for stationary and dynamic contact; an apparatus has been developed to experimentally validate these models. This paper focuses on validation of the normal contact models. Measurements of forces and displacements will be used to identify the parameters related to the normal force, i.e. the volumetric stiffness and hysteretic damping factor for metallic surfaces. The experimental measurements are compared with simulated results to assess the validity of the volumetric model.

Commentary by Dr. Valentin Fuster
2011;():285-293. doi:10.1115/DETC2011-47146.

A large body of literature exists regarding linear and nonlinear dynamic absorbers, but the vast majority of it deals with linear primary structures. However, nonlinearity is a frequent occurrence in engineering applications. Therefore, the present paper focuses on the mitigation of vibrations of nonlinear primary systems using nonlinear dynamic absorbers. Because most existing contributions about their design rely on extensive parametric studies, which are computationally demanding, or on analytic methods, which may be limited to small-amplitude motions, this study proposes a tuning procedure which is computationally tractable and can treat strongly nonlinear regimes of motion. The proposed methodology relies on a frequency-energy based approach followed by bifurcation analysis. The results are illustrated using a one-degree-of-freedom primary system, which can, for instance, represent the vibrations of a specific mode of a multi-degree-of-freedom structure.

Commentary by Dr. Valentin Fuster
2011;():295-304. doi:10.1115/DETC2011-47207.

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

Commentary by Dr. Valentin Fuster
2011;():305-315. doi:10.1115/DETC2011-47276.

This paper discusses the problem of control constraint realization applied to the design of maneuvers of complex under-actuated systems modeled as multibody problems. Applications of interest in the area of aerospace engineering are presented and discussed. The tangent realization of the control constraint is discussed from a theoretical point of view and used to determine feedforward control of realistic under-actuated systems. The effectiveness of the computed feedforward input is subsequently verified by applying it to more detailed models of the problems, in presence of disturbances and uncertainties in combination with feedback control. The proposed applications consist in the position control of a complex closed chain mechanism representative of a robotic system, the control of a simplified model of a canard and a conventional air vehicle in the vertical plane, and the angular velocity control of a wind-turbine. In the aeromechanics examples, the tangent realization of the control relies on the availability of the Jacobian matrix of an aeroelastic model. All problems are solved using a free general-purpose multibody software that writes the constrained dynamics of multi-field problems in form of Differential-Algebraic Equations (DAE). The equations are integrated using A/L-stable algorithms. The essential extension to the multibody code consisted in the addition of the capability to write arbitrary constraint equations and apply the corresponding reaction multipliers to arbitrary equations of motion. This allowed to exploit the modeling capabilities of the formulation without any undue restriction on the modeling requirements.

Commentary by Dr. Valentin Fuster
2011;():317-326. doi:10.1115/DETC2011-47310.

The formulation of multibody dynamics in terms of natural coordinates (NCs) leads to equations of motion in the form of differential-algebraic equations (DAEs). A characteristic feature of the natural coordinates approach is a constant mass matrix. The DAEs make possible (i) the systematic assembly of open-loop and closed-loop multibody systems, (ii) the design of state-of-the-art structure-preserving integrators such as energy-momentum or symplectic-momentum schemes, and (iii) the direct link to nonlinear finite element methods. However, the use of NCs in the optimal control of multibody systems presents two major challenges. First, the consistent application of actuating joint-forces becomes an issue since conjugate joint-coordinates are not directly available. Secondly, numerical methods for optimal control with index-3 DAEs are still in their infancy. The talk will address the two aforementioned issues. In particular, a new energy-momentum consistent method for the optimal control of multibody systems in terms of NCs will be presented.

Commentary by Dr. Valentin Fuster
2011;():327-335. doi:10.1115/DETC2011-47502.

In this paper, a nonlinear controller design for constrained systems described by Lagrangian differential algebraic equations (DAEs) is presented. The controller design utilizes the structure introduced by the coordinate splitting formulation, a numerical technique used for integration of DAEs. In this structure, the Lagrange multipliers associated with the constraint equations are eliminated, and the equations of motion are transformed into implicit differential equations. Making use of this, a feedback linearizing controller can be chosen for successful motion tracking of the constrained system. Numerical examples demonstrate the controller design can be successfully applied to fully actuated and underactuated systems.

Commentary by Dr. Valentin Fuster
2011;():337-346. doi:10.1115/DETC2011-47578.

Efficient and reliable sensitivity analyses are critical for topology optimization, especially for multibody dynamics systems, because of the large number of design variables and the complexities and expense in solving the state equations. This research addresses a general and efficient sensitivity analysis method for topology optimization with design objectives associated with time dependent dynamics responses of multibody dynamics systems that include nonlinear geometric effects associated with large translational and rotational motions. An iterative sensitivity analysis relation is proposed, based on typical finite difference methods for the differential algebraic equations (DAEs). These iterative equations can be simplified for specific cases to obtain more efficient sensitivity analysis methods. Since finite difference methods are general and widely used, the iterative sensitivity analysis is also applicable to various numerical solution approaches. The proposed sensitivity analysis method is demonstrated using a truss structure topology optimization problem with consideration of the dynamic response including large translational and rotational motions. The topology optimization problem of the general truss structure is formulated using the SIMP (Simply Isotropic Material with Penalization) assumption for the design variables associated with each truss member. It is shown that the proposed iterative steps sensitivity analysis method is both reliable and efficient.

Commentary by Dr. Valentin Fuster
2011;():347-354. doi:10.1115/DETC2011-47707.

In industrial manipulators and machine tools modern lightweight designs result in low energy consumption and often allow high working speeds. However, undesired vibrations occur due to the flexibility of the bodies and the control of flexible multibody systems is often a challenging task. In order to achieve good end-effector tracking performance the mechanical design and the control design must be considered concurrently in the sense of an integrated design process. In this paper three different optimization based integrated design approaches for controlled flexible multibody systems are presented.

Commentary by Dr. Valentin Fuster
2011;():355-360. doi:10.1115/DETC2011-48229.

This work presents a novel nonlinear programming based motion planning framework that treats uncertain fully-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; ignoring uncertainty during design may lead to poor robustness and suboptimal performance. System uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, new design questions related to uncertain dynamical systems can now be answered through the new framework. Specifically, this work presents the new framework through an inverse dynamics formulation where deterministic state trajectories are prescribed and uncertain actuator inputs are quantified. The benefits of the ability to quantify the resulting actuator uncertainty are illustrated in a time optimal motion planning case-study of a serial manipulator pick-and-place application. The resulting design determines a feasible time optimal motion plan—subject to actuator and obstacle avoidance constraints—for all possible systems within the probability space. The forward dynamics formulation (using deterministic actuator inputs and uncertain state trajectories) is presented in a companion paper.

Commentary by Dr. Valentin Fuster
2011;():361-366. doi:10.1115/DETC2011-48336.

A new command-shaping control strategy for oscillation reduction of damped harmonic oscillators is derived and implemented on damped overhead cranes. The effect of damping on the shaper frequency and duration is investigated. The performance of the proposed simper is simulated numerically and compared with the classical double-step input-shaper for different system properties. It was shown that, the proposed wave-form command profiles are capable of eliminating the travel and residual oscillations for systems with different damping ratio. Further, unlike traditional impulse and step command shapers, the proposed command profiles have smoother intermediate acceleration, velocity, and displacement profile.

Topics: Gantry cranes , Waves
Commentary by Dr. Valentin Fuster
2011;():367-375. doi:10.1115/DETC2011-48400.

Traditionally, multi-mode command-shaping controllers are tuned to the system frequencies. This work suggests an opposite approach. A frequency-modulation (FM) strategy is developed to tune the system frequencies to match the frequencies eliminated by a single-mode command-shaper. The shaper developed in this work is based on a double-step command-shaping strategy. Using the FM Shaper, a simulated feedback system is used to modulate the closed-loop frequencies of a simulated double-pendulum model to the point where the closed-loop second mode frequency becomes an odd multiple of the closed-loop first mode frequency, which is the necessary condition for a satisfactory performance of a single-mode command-shaper. The double-step command-shaper is based on the closed-loop first mode frequency. The input commands to the plant of the simulated closed-loop system are then used to drive the actual double-pendulum. Performance is validated experimentally on a scaled model of a double-pendulum gantry crane.

Commentary by Dr. Valentin Fuster
2011;():377-382. doi:10.1115/DETC2011-48533.

This paper aims to generalize the computed torque control method for underactuated systems which are modeled by a non-minimum set of generalized coordinates subjected to geometric constraints. The control task of the underactuated robot is defined in the form of servo constraint equations that have the same number as the number of independent control inputs. A PD controller is synthesized based on projecting the equations of motion into the nullspace of the distribution matrix of the actuator forces/torques. The results are demonstrated by numerical simulation and experiments conducted on a two degrees-of-freedom device.

Commentary by Dr. Valentin Fuster
2011;():383-391. doi:10.1115/DETC2011-48551.

An essential requirement in haptics is accuracy and transparency of the haptic interface. Haptic devices are usually lightweight robotic systems with which a human operator interacts. In the current literature, dynamic analyses of haptic devices are limited to single degree-of-freedom (DoF) point mass models. In this paper, experimental and simulation studies are conducted to investigate the effects of mechanical design parameters on the performance of such devices. For this purpose two commonly used haptic devices were considered: a two-DoF PANTOGRAPH and a three-DoF PHANToM. The results show that dynamic coupling between the rendered (controlled) and free directions of motion can influence the desired performance. An alternative formulation is outlined in which dynamic behavior of a haptic interface is modeled as a multibody system. The dynamic equations are separated to two sets of equations associated with the rendered and admissible motions. Effects of time delay and discretization stemming from digital realization of the virtual environment can be analyzed using the rendered dynamic equations, while the equations associated with the admissible motions can serve as a basis for performance measure. This formulation can be efficiently used for the complex nonlinear dynamics and stability analyses of haptic interfaces and can provide essential details on the performance of these devices. Stability analysis of a two-DoF five-bar linkage is presented as an example using the proposed formulation.

Commentary by Dr. Valentin Fuster
2011;():393-402. doi:10.1115/DETC2011-48750.

This paper presents the implementation of a numerical algorithm for the direct solution of optimal control and parameter identification problems. The problems may include differential equations that define the state, inequality constraints, and equality constraints at the initial and final times. The numerical method is based on transforming the infinite dimensional optimal control problem into a finite dimensional nonlinear programming problem. The transformation technique involves dividing the time interval of interest into a mesh that need not be uniform. In each subinterval of the mesh the control input is approximated using a piecewise polynomial. In particular, the control can be approximated using: (i) piecewise constant, (ii) piecewise linear, or (iii) piecewise cubic polynomials. The explicit Runge-Kutta method is used to obtain an approximate solution of the differential equations that define the state. With the approach used here the states do not appear in the nonlinear programming (NLP) problem. As a result the NLP problem is very compact relative to other numerical methods used to solve nonlinear optimal control problems. The NLP problem is solved using a sequential quadratic programming (SQP) technique. The SQP method is based on minimizing the L1 exact penalty function. Each major step of the SQP method solves a strictly convex quadratic programming problem. The paper also describes a simplified interface to the computer programs that implement the method. An example is presented to demonstrate the algorithm.

Commentary by Dr. Valentin Fuster
2011;():403-410. doi:10.1115/DETC2011-48884.

This paper presents a generalization of the divide and conquer algorithm for sensitivity analysis of dynamic multibody systems based on direct differentiation. While similar sensitivity analysis approach has been demonstrated for multi-rigid and multi-flexible systems in tree topologies and a limited set of kinematically closed loop topologies, this paper presents the generalization of these approaches to systems in generalized topologies including many coupled kinematically closed loops. This generalization retains the efficient complexity of the underlying formulations i.e. linear and logarithmic complexity in serial and parallel implementation. Other than the computational efficiency, the advantages of this method include concurrent sensitivity analysis with forward dynamics, no numerical artifacts arising from parametric perturbation and significantly reduced data storage compared to traditional methods. An interesting application of this work in control of multibody systems is discussed.

Commentary by Dr. Valentin Fuster
2011;():411-418. doi:10.1115/DETC2011-48989.

Many systems have, by their nature, a small damping and therefore they are potentially subjected to dangerous vibration phenomena. The aim of active vibration control is to contain this phenomenon, increasing the damping of the system without changing its natural frequencies and vibration modes. A control of this type can improve the dynamic performance, reduce the vibratory phenomenon (and the resulting acoustic noise) and increase the fatigue strength of the system. The paper introduces a new approach to the synthesis of a modal controller to suppress vibrations in structures: it turns from the traditional formulation of the problem showing how the performance of the designed controller can be evaluated through the analysis of the resulting modal damping matrix of the controlled system. Such analysis allows to evaluate spillover effects, due to the presence of un-modeled modes, the stability of the control and the consequent effectiveness in reducing vibration. The ability to easily manage this information allows the synthesis of an efficient modal controller. Theoretical aspects are supported by experimental applications on a large flexible system.

Commentary by Dr. Valentin Fuster
2011;():419-425. doi:10.1115/DETC2011-47312.

Virtual stick balancing (VSB) is a manual visuomotor tracking task that involves interplay between a human and a computer in which the movements are programmed to resemble those of balancing a stick at the fingertip. Since time delays and random perturbations (“noise”) are intrinsic properties of this task, we modeled VSB as a delayed pursuit-escape process: the target movements are described by a simple random walk and those movements controlled by the computer mouse by a delayed random walk biased towards the target. As subjects become more skilled, a stereotyped and recurring pursuit-escape pattern develops in which the mouse pursues the target until it overtakes it, causing the target to move in a different direction, followed, after a lag, by the pursing mouse. The delayed pursuit-escape random walk model captured the qualitative nature of this tracking task and provided insights into why this tracking task always fails at some point in time, even for the most expert subjects.

Commentary by Dr. Valentin Fuster
2011;():427-436. doi:10.1115/DETC2011-47347.

In this paper we investigate synchronization of oscillators. We use mechanical metronomes that are coupled through a mechanical medium. In passive coupling of two oscillators, the coupling medium is a one degree of freedom passive mechanical basis. The analysis of the system is shown and supported by simulations of the proposed model and experimental results. We show how the oscillators synchronize and discuss the affecting parameters in synchronization. In another case, the oscillators are forced by an external input while that input is also affected by the oscillators. This feedback loop introduces dynamics to the whole system. For this case, we place the mechanical metronomes on a one degree of freedom moving base. The movements of the base are a function of a feedback from the phases of the metronomes. We study the space of possibilities for the movements of the base and consider impacts of the base movement on the synchronization of metronomes. We also show how such a system evolves in time when we introduce an adjusting parameter that changes over time and updates based on feedbacks from the system.

Topics: Synchronization
Commentary by Dr. Valentin Fuster
2011;():437-446. doi:10.1115/DETC2011-47391.

In this paper, we deal with the nonlinear dynamics, the transfer of energy and control of the vibrations of a Micro Electro-mechanical System (MEMS) gyroscope. The MEMS are micro-transducers whose operation is based on elastic and electrostatic forces that convert electrical energy into mechanical energy and vice-versa. These systems can be modeled by 2-DOF spring-mass-damper system and the coupling of the system equations is performed by Coriolis force. This coupling is responsible for the energy transfers of the two vibration modes (drive-mode and sense-mode) and for the resonance in MEMS gyroscope. The governing equations of motion have periodic coefficients and as the dimensions of the quantities involved in the system may be inconsistent it is not advisable the use of perturbation methods for the solution of the MEMS gyroscope. For this reason, in the dynamic analysis and control of the vibrations of the MEMS gyroscope, we used a technique based on Chebyshev polynomial expansion, the iterative Picard and transformation of Lyapunov-Floquet (L–F). For the analysis of the dynamic of the micro electro-mechanical system gyroscope, we did the diagram of stability, phase planes and time history of transfer of energy. Finally, we did the control of the unstable orbit to a desired periodic one and compared the phase planes of orbits desired and controlled and time histories of energy transfer of the controlled and non-controlled system.

Commentary by Dr. Valentin Fuster
2011;():447-456. doi:10.1115/DETC2011-47519.

This paper describes and compares the zeroth-order semi-discretization, spectral element, and Legendre collocation methods. Each method is a technique for solving delay differential equations (DDEs) as well as determining regions of stability in the DDE parameter space. We present the necessary concepts, assumptions, and equations required to implement each method. To compare the relative performance between the methods, the convergence rate achieved and computing time required by each method are determined in two numerical studies consisting of a ship stability example and the delayed damped Mathieu equation. For each study, we present a stability diagram in parameter space and a convergence plot. The spectral element method is demonstrated to have the quickest convergence rate while the Legendre collocation method requires the least computing time. The zeroth-order semi-discretization method on the other hand has both the slowest convergence rate and requires the most computing time.

Commentary by Dr. Valentin Fuster
2011;():457-466. doi:10.1115/DETC2011-47671.

In this paper, the analysis of delay differential equations with periodic coefficients and discontinuous distributed delay is carried out through discretization by Chebyshev spectral continuous time approximation (ChSCTA). These features are introduced in the delayed Mathieu equation with discontinuous distributed delay used as an illustrative example. The efficiency of the process of stability analysis is improved by using shifted Chebyshev polynomials for computing the monodromy matrix, as well as the adaptive meshing of the parameter plane. An idea for a method for numerical integration of periodic DDEs with discontinuous distributed delay based on existing MATLAB functions is proposed.

Commentary by Dr. Valentin Fuster
2011;():467-473. doi:10.1115/DETC2011-47745.

The linearly varied helix tool is widely used in manufacturing industry and milling tools are available in the market with these special cutting edges. There were several attempts to introduce complex harmonically varied helix tools, but the manufacturing of sinusoid edges is extremely difficult and its effect on cutting dynamics is not clear yet. In this study a mechanical model is introduced to predict the linear stability of these special cutters. It is shown that these milling tools cause distribution in regeneration and the corresponding time periodic distributed delay differential equations are investigated by semi-discretization. This work points out how the harmonically varied helix cutters behave in case of high and low cutting speed applications.

Topics: Stability , Milling
Commentary by Dr. Valentin Fuster
2011;():475-482. doi:10.1115/DETC2011-47795.

To analyze the excitation mechanism of self-excited oscillation in a beam which is in contact with a moving floor surface, we deal with a beam subjected to Coulomb friction and theoretically predict the occurrence of self-excited oscillation through flutter-type instability. We introduced an extensible continuum model, and derived its governing equations by special Cosserat theory, which allows for the extensibility of the beam to be considered and boundary conditions. The boundary conditions on the end of the beam are unique, because the end of the beam contacts with the moving floor surface. Then, we discretized the system, analyzed the linear stability, and indicated that the flutter-type instability in the beam is produced due to the Coulomb friction and the extension of the extensibility.

Commentary by Dr. Valentin Fuster
2011;():483-492. doi:10.1115/DETC2011-47832.

Precision and stability in position control of robots are critical parameters in many industrial applications where high accuracy is needed. It is well known that digital effect is destabilizing and can cause instabilities. In this paper, we analyze a single DoF system and we present the stability limits in the parameter space of the control gains. Furthermore we introduce a nonlinearity relative to the saturation of the control force in the model, reduce the dynamics of the nonlinear map to its local center manifold, study the bifurcation along the stability border and identify conditions under which a supercritical or subcritical bifurcation occurs. The obtained results explain some of the typical instabilities occurring in industrial applications. We verify the obtained results through numerical simulations.

Commentary by Dr. Valentin Fuster
2011;():493-501. doi:10.1115/DETC2011-47870.

The non linear system under study consists on the bouncing ball problem. Focusing on the n-T periodic solutions and the permanent contact motion, simulations performed underline the effect of spring-damper contact model in comparison with the classical restitution coefficient. Both approaches are implemented in an adimensional way. For the restitution coefficient approach, iterating maps are easy to obtain after some assumptions. On the contrary, the spring-damper model leads to transcendental equations needing the use of numerical continuation methods. The damping ratio is defined as a function of the restitution coefficient. The effect of the contact stiffness is studied. For high values of the contact stiffness, the spring-damper model has the same behavior as the restitution coefficient model as the impact duration gets shorter. Predictions of the two models diverge when the contact stiffness decreases. Results are illustrated by time histories and Poincaré Maps of dynamic responses. This paper aims to be guideline to quantify the error made by making the assumptions required for a restitution coefficient model.

Topics: Dampers , Springs
Commentary by Dr. Valentin Fuster
2011;():503-510. doi:10.1115/DETC2011-47890.

When a semi-infinite cable resting on a bed of unilateral springs is subjected to a harmonic excitation, the motion of the touch-down-point (TDP), i.e., the point which separates the detached part of the cable from the laid part, and which is assumed to be unique in this paper, exhibits interesting resonant phenomena. These phenomena are studied numerically by means of a self-made finite element (FEM) code, and the effects of the non-linearity of the problem, such as, e.g., the bending of the resonance curves and the secondary resonances, are investigated in detail.

Commentary by Dr. Valentin Fuster
2011;():511-520. doi:10.1115/DETC2011-48179.

The vibrations inevitably occur while milling of the details with insufficient rigidity like the turbine blades for engines and various propulsion systems. This effect is undesirable as it decreases accuracy and the machined surface quality. The vibrations suppression is realized by applying additional damping or by choosing cutting conditions ensuring the process stability. In general the problem is solved by the determination of the process stability lobes. This criterion assumes that process is stable if the regenerative vibrations of tool or workpiece are damped. The additional criterion is discussed in the paper — the roughness of the machined surface. For this purpose authors elaborated the algorithm of the numerical simulation of milling process, considering the dynamics of tool and workpiece and applying the algorithm of machined surface geometrical modeling that takes into account the delay mechanism inherent to the process. The numerical solution of the simplified model in the given paper is considered. The Poincare’s maps of the vibration amplitudes, the machined surface errors, and the cutting force magnitudes depending on cutting conditions are presented. Authors conclude, that in general the vibration stability while milling process is not the absolute quality criterion. The combination of the developed criteria is introduced.

Topics: Stability , Milling
Commentary by Dr. Valentin Fuster
2011;():521-527. doi:10.1115/DETC2011-48300.

The standard models of the milling process describe the surface regeneration effect by a delay-differential equation with constant time delay. In this study, an improved two degree of freedom model is presented for milling process where the regenerative effect is described by an improved state dependent time delay model. The model contains exact nonlinear screen functions describing the entrance and exit positions of the cutting edges of the milling tool. This model is valid in case of large amplitude forced vibrations close to the near-resonant spindle speeds. The periodic motions of this nonlinear system are calculated by a shooting method. The stability calculation is based on the linearization of the state-dependent delay differential equation around these periodic solutions by means of the semi-discretization method. The results are validated by an advanced numerical time domain simulation where the chip thickness is calculated by means of Boolean algebra.

Topics: Bifurcation , Delays , Milling
Commentary by Dr. Valentin Fuster
2011;():529-538. doi:10.1115/DETC2011-48829.

A general class of car-following models is analyzed where the longitudinal acceleration of a vehicle is determined by a nonlinear function of the distance to the vehicle in front, their velocity difference, and the vehicle’s own velocity. The driver’s response to these stimuli includes the driver reaction time that appears as a time delay in governing differential equations. The linear stability of the uniform flow is analyzed for human-driven and computer-controlled (robotic) vehicles. It is shown that the stability conditions are equivalent when considering ring-road and platoon configurations. It is proven that time delays result in novel high-frequency oscillations that manifest themselves as short-wavelength traveling waves. The theoretical results are illustrated using an optimal velocity model where the nonlinear behavior is also revealed by numerical simulations. The results may lead to better understanding of multi-vehicle dynamics and allow one to design cooperative autonomous cruise control algorithms.

Commentary by Dr. Valentin Fuster
2011;():539-550. doi:10.1115/DETC2011-48891.

This study investigates the dynamics of planetary gears where nonlinearity is induced by bearing clearance. Lumped-parameter and finite element models of planetary gears with bearing clearance, tooth separation, and gear mesh stiffness variation are developed. The harmonic balance method with arc-length continuation is used to obtain the dynamic response of the lumped-parameter model. Solution stability is analyzed using Floquet theory. Rich nonlinear behavior is exhibited in the dynamic response, consisting of nonlinear jumps and a hardening effect induced by the transition from no bearing contact to contact. The bearings of the central members (sun, ring, and carrier) impact against the bearing races near resonance, which leads to coexisting solutions in wide speed ranges, grazing bifurcation, and chaos. Secondary Hopf bifurcation is the route to chaos. Input torque can significantly suppress the nonlinear effects caused by bearing clearance.

Commentary by Dr. Valentin Fuster
2011;():551-560. doi:10.1115/DETC2011-47030.

Most of researches in the field of bicycle dynamics deal with auto-stabilization and rider control by means of steer-torque and lean-torque. Bicycle models composed by rigid bodies with thin wheels making point contact with the road and rolling without any slip are suited for carrying out these studies. Numerical analysis of stability by means of these models leads to the capsize, castering and weave modes, which make it possible to understand many aspects of bicycle dynamics. However, some high performance bicycles at high speed show dangerous wobble oscillations. Cyclists’ experience and recent researches highlight that wobble phenomena are related both to tire properties and to fork and frame compliance. Since structural compliance in dynamic conditions generates vibrations, this paper focuses on the study of structural vibrations of high performance bicycles with the modal analysis approach. To isolate the effects of frame and fork compliance, four particular bicycles are considered, they are built assembling a pair of wheels, two forks (fork A and B) with the same shape but different structures and materials and two frames (frame A and B) with the same shape but different structures. Preliminary road tests showed that bicycles made with components A are more prone to wobble oscillations. In order to have a better comprehension of the different influence of fork and frame compliance, first the two forks (with the front wheel) are modally tested with the steer tube locked to a very stiff structure, then, the whole bicycles are tested. Modal analysis is carried out with the impulse method, for the analysis of each bicycle 60 FRFs are measured. The results of modal analysis are presented and the influence of identified modes on bicycle stability is discussed. An important issue of modal analysis of vehicles is the correlation between modal tests carried out in the laboratory and bicycle behavior on the road. When the vehicle is tested in the laboratory, additional constraints are added to guarantee equilibrium, but centrifugal forces are not present, because the vehicle is stationary. Since the analysis of the equations of linearized dynamics shows that the stiffness matrix includes a part due to centrifugal effects, the additional stiffness terms due to constraints in laboratory tests can be assumed to be equivalent to the centrifugal terms of the stiffness matrix at a certain speed. Details and limits of this equivalence are presented and discussed in the paper.

Topics: Bicycles
Commentary by Dr. Valentin Fuster
2011;():561-569. doi:10.1115/DETC2011-47344.

In 2007, Meijaard, et al. [1] presented the canonical linearized equations of motion for the Whipple bicycle model along with test cases for checking alternative formulations of the equations of motion or alternative numerical solutions. This paper describes benchmarking three other implementations of bike equations of motion: the linearized equations for bicycles written by Papadopoulos and Schwab [2] in JBike6, the non-linear equations for bicycles outlined by Schwab [3] and implemented in MATLAB as a Cornell University class project, and the non-linear equations for motorcycles implemented in FastBike from the Motorcycle Dynamics Research Group at the University of Padua. [4] Some implementations are easier to benchmark than others. For example, JBike6 is designed to produce eigenvalues and easily exposes the coefficients of its linearized equations of motion. At the other extreme, the class project non-linear equations were not originally intended to generate eigenvalues and are implemented in a single 48×48 matrix. Finally, while FastBike does generate eigenvalues, its equations of motion incorporate tire and frame compliance, which cannot be completely disabled. Instead, the tire stiffness parameters must be increased, but not so much as to cause convergence errors in FastBike. In the end, all three implementations generate eigenvalues that match the published benchmark values to varying degrees. JBike6 comes the closest, with agreement of 12 digits or more. The class project is second, with agreement of 12 digits for most forward speeds, but with a loss of measurable agreement near the capsize speed due to a peak in the eigenvalue condition number. Unfortunately, FastBike is limited at this time to exporting eigenvalues with no more than two decimal places, and so agreement can only be found to ±0.005.

Commentary by Dr. Valentin Fuster
2011;():571-579. doi:10.1115/DETC2011-47359.

Perturbation analysis and chaotic dynamics of the rotating blade with varying angular speed are investigated. Centrifugal force, aerodynamic load and the perturbed angular speed due to the inconstant air velocity are considered. The rotating blade is treated as a pre-twist, presetting, thin-walled rotating cantilever beam. The nonlinear governing partial differential equations of the varying angular rotating blade are established by using Hamilton’s principle. Then, the ordinary differential equations of the rotating blade are obtained by employing the Galerkin’s approach during which Galerkin’s modes satisfy corresponding boundary conditions. The four-dimensional nonlinear averaged equations are obtained by applying the method of multiple scales. In this paper, the resonant case is 1:2 internal resonance-1/2 subharmonic resonance. The numerical simulation is used to investigate chaotic dynamics of the varying angular rotating blade. The results show that the system is sensitive to the rotating speed and there are chaotic motions.

Commentary by Dr. Valentin Fuster
2011;():581-588. doi:10.1115/DETC2011-47463.

Unicycles are inherently unstable vehicles and require longitudinal and lateral control including pitch and roll motion. The one wheel is propelled by the rider and provides the longitudinal motion and the pitch control of the vehicle as well. The roll control is achieved by balancing carried out by the rider since the nonholonomic constraint does not allow a lateral displacement of the wheel–guideway contact point. Usually, forces and torques are used as control inputs even if human motions are mainly position controlled by visual feedback and not force controlled. In this paper the roll motion of a unicycle is considered. The balancing is obtained by the upper body’s roll motion which is used as control input. It is shown that balancing can be modeled by an inverted double pendulum where the relative acceleration of the upper body is chosen as control variable. Due to the nominal vertical position of the unicycle running straight ahead the balancing is represented by linear equations of motion and linear control theory is applied. It turns out that from simulations and experiments that properly controlled body positioning ensures balancing, too.

Commentary by Dr. Valentin Fuster
2011;():589-596. doi:10.1115/DETC2011-47540.

In this investigation, a numerical procedure that can be used for solving complex wheel/rail contact problems in turnout is proposed. In particular, a combined nodal and non-conformal contact approach is developed such that significant jumps in contact points are detected using the nodal search, while the exact location of contact point is then determined with continuous surface parameterizations using non-conformal contact equations. With this combined nodal and non-conformal contact approach for the contact geometry analysis of vehicle/turnout interactions, multiple look-up contact tables can be generated in an efficient way without losing accuracy. Since detailed contact search is performed offline to obtain look-up contact tables, significant changes in contact points in turnout can be efficiently predicted online with tabular data to be interpolated in a standard way. Several numerical examples are presented in order to demonstrate the use of the numerical procedure developed in this investigation.

Topics: Vehicles , Railroads
Commentary by Dr. Valentin Fuster
2011;():597-607. doi:10.1115/DETC2011-47963.

This paper gives an overview on handling aspects in bicycle and motorcycle control, from both theoretical and experimental points of view. Parallels are drawn with the literature on aircraft handling. The paper concludes with the open ends and promising directions for future work in the field of handling and control of single track vehicles.

Topics: Bicycles , Motorcycles
Commentary by Dr. Valentin Fuster
2011;():609-615. doi:10.1115/DETC2011-48019.

This paper deals with a dynamic analysis of a racing kart considering an elastic deformation of the kart frame. As the first step of this research, the FEM kart frame model was validated by means of static and dynamic tests. In the static test, the strain on the kart frame caused by a steering operation was measured by strain gauges, and compared to the simulation result. The dynamic response of the frame was evaluated by hammering test, and the result was compared to the modal analysis result. Next, a flexible multibody vehicle model was developed with this FEM frame model. In this process, model reduction based on the modal analysis is applied to reduce the degree of freedom of the flexible body. Some running tests with actual racing kart were carried out to evaluate the handling characteristic, and the comparison between simulation and experiment are discussed.

Commentary by Dr. Valentin Fuster
2011;():617-627. doi:10.1115/DETC2011-48212.

The stability analysis of railroad vehicles using eigenvalue analysis can provide essential information about the stability of the motion, ride quality or passengers comfort. The system eigenvalues are not in general a vehicle property but a property of a vehicle travelling steadily on a periodic track. Therefore the eigenvalue analysis follows three steps: calculation of steady motion, linearization of the equations of motion and eigenvalue calculation. This paper deals with different numerical methods that can be used for the eigenvalue analysis of multibody models of railroad vehicles that can include deformable tracks. Depending on the degree of nonlinearity of the model, coordinate selection or the coordinate system used for the description of the motion, different methodologies are used in the eigenvalue analysis. A direct eigenvalue analysis is used to analyse the vehicle dynamics from the differential-algebraic equations of motion written in terms of a set of constrained coordinates. In this case not all the obtained eigenvalues are related to the dynamics of the system. As an alternative the equations of motion can be obtained in terms of independent coordinates taking the form of ordinary differential equations. This procedure requires more computations but the interpretation of the results is straightforward.

Commentary by Dr. Valentin Fuster
2011;():629-640. doi:10.1115/DETC2011-48313.

The dynamic performance of vehicle drivetrains is significantly influenced by differentials which are subjected to complex phenomena. In this paper, detailed models of TORSEN differentials are presented using a flexible multibody simulation approach, based on the nonlinear finite element method. A central and a front TORSEN differential have been studied and the numerical results have been compared with experimental data obtained on test bench. The models are composed of several rigid and flexible bodies mainly constrainted by flexible gear pair joints and contact conditions. The three differentials of a four wheel drive vehicle have been assembled in a full drivetrain in a simplified vehicle model with modeling of driveshafts and tires. These simulations enable to observe the four working modes of the differentials with a good accuracy.

Commentary by Dr. Valentin Fuster
2011;():641-647. doi:10.1115/DETC2011-48440.

Simulating mobile robots in unstructured environments requires knowledge of the wheel/terrain interaction phenomena. Even assuming that the terramechanics models available accurately represent the physics of the interaction, estimation of soil parameters can be a source of error. In applications where high robot reliability is mandatory, it is important to realize the influence of possible sources of error on the system behavior. The effect of small variations of parameters on system performance can be studied under sensitivity analysis. In this work, sensitivity analysis is conducted to investigate the effect of perturbations in the soil parameters on the behavior of a single rigid wheel and a vehicle on soft terrain. For the first system the two widely used terramechanics models, Bekker’s and Wong and Reace’s are studied, sensitivity analysis being conducted using direct differentiation. The second system is modeled using Bekker model, sensitivity being obtained using finite differences.

Commentary by Dr. Valentin Fuster
2011;():649-656. doi:10.1115/DETC2011-47183.

Classical mechanics is mainly based on two mechanical principles, the principle of linear momentum (Isaac Newton) and the principle of angular momentum (Leonhard Euler). The principle of angular momentum implies that the time derivative of the angular momentum equals the sum of all torques, acting on the body. Concerning all types of education it is particularly important that theoretical basic principles are profoundly understood. This often enables to understand difficult mechanical systems by drawing parallels between complex mechanical systems and simple basic principles. One way to generate profound understanding of theoretical correlations is to use interesting experimental examples. In this paper, a teaching model is presented, which has the ability both to demonstrate the effects of the principle of angular momentum and to catch the attention of students. For this purpose, a remote-controlled model car was built carrying a high-speed gyroscope on its top. The gyroscope can cause that the car turns over to the inside of a turn against the centrifugal force. Even more, it is possible to drive in a circle on the inner tires of the RC vehicle.

Topics: Vehicles
Commentary by Dr. Valentin Fuster
2011;():657-665. doi:10.1115/DETC2011-48351.

Among the many different approaches to teach engineering subjects, the project-based methodology turns out to be one of the most effective ones. In the field of undergraduate numerical methods, it can overcome some of its inherent difficulties. This paper considers a particular context: a general 90-hour numerical methods subject in an Industrial-Mechanical Engineering degree. The methods are applied to mechanical engineering problems such as matrix structural analysis, finite element method, multibody systems (MBS), harmonic analysis, or optimization. The article suggests how an appropriate formulation and a practical MATLAB™-based project make up a good approach for a short-time practical training on multibody dynamics (MBD) within that subject. The keys to the theoretical lessons and an example of the project are explained thoroughly. The mechanical project has to be rich in numerical methods. MBD and the finite element method fulfill this requirement. The former is chosen in this article. The students know the basics, but they have to learn everything about MBD in very little time. This experience can be useful in other educational contexts. After explaining the approach, some sample assignment exercises are described, as well as a possible way to assess the work of the students. The result of this approach is a reasonable achievement-time tradeoff shown in the solid skills acquired by the students and proven by the experience of the last few years.

Commentary by Dr. Valentin Fuster
2011;():667-673. doi:10.1115/DETC2011-48355.

This paper presents a modeling and simulation framework for tracked vehicles for ride comfort and load prediction analysis. The development began with the identification of the key issues such as formulations, integration schemes and contact (with friction) modeling on which the comparative studies are conducted. Based on the results of the investigations, the framework and process for the modeling and simulation of tracked vehicles are established and appropriate algorithms for contact and friction are developed. To facilitate the modeling and simulation process, a Python-based modeling environment was developed for process automation and design optimization. The developed framework has been successfully applied to the dynamic load predication of a military tracked vehicle. The parameter optimization enabled with the Python-based process automation tool helps improve the design and modification of vehicles for significantly improved fatigue life of suspension component.

Commentary by Dr. Valentin Fuster
2011;():675-687. doi:10.1115/DETC2011-48743.

A flexible multibody dynamics explicit time-integration parallel solver suitable for real-time virtual-reality applications is presented. The hierarchical “scene-graph” representation of the model used for display and user-interaction with the model is also used in the solver. The multibody system includes rigid bodies, flexible bodies, joints, frictional contact constraints, actuators and prescribed motion constraints. The rigid bodies rotational equations of motion are written in a body-fixed frame with the total rigid body rotation matrix updated each time step using incremental rotations. Flexible bodies are modeled using total-Lagrangian spring, truss, beam and hexahedral finite elements. The motion of the elements is referred to a global inertial Cartesian reference frame. A penalty technique is used to impose joint/contact constraints. An asperity-based friction model is used to model joint/contact friction. A bounding box binary tree contact search algorithm is used to allow fast contact detection between finite elements and other elements as well as general triangular/quadrilateral rigid-body surfaces. The real-time solver is used to model virtual-reality based experiments (including mass-spring systems, pendulums, pulley-rope-mass systems, billiards, air-hockey and a solar system) for a freshman university physics e-learning course.

Commentary by Dr. Valentin Fuster
2011;():689-694. doi:10.1115/DETC2011-47083.

One of the main challenging tasks in the modern design of highly adaptive granular material is in ability to passively control the flow of energy through it by means of trapping, redirection and scattering. In the present work we demonstrate that one of the possible mechanisms to achieve efficient control over the propagating shock wave in the material is the usage of weakly interacting, non-compressed granular lens (granular chains). In the latest computational studies we have demonstrated that the shock waves initially localized on a finite amount of chains may be efficiently redirected to the neighboring granular chains. In this study it is also shown that the amplitude of the shock wave redirected to the neighboring chains may be passively controlled by choosing appropriate parameters of coupling which makes this type of granular structure highly adaptive for the required control of mechanical energy flow. The mechanism for efficient transport of energy from one chain to another are also found. It corresponds to a simple exchange of energy between the weakly interacting granular chains providing equi-partition of Nesterenko solitary waves through the chains. This mechanism of energy transfer and redirection in highly nonlinear granular chains are conceptually new. Analytical and computational studies of all the mechanisms are performed in the present study.

Commentary by Dr. Valentin Fuster
2011;():695-702. doi:10.1115/DETC2011-47084.

It is a well known fact that many interesting phenomena in the theory of waves in nonlinear lattices, e.g., the significant reduction of the amplitude of a propagating primary pulse or the essential growth of the phase velocity, may be explained in terms of various resonant mechanisms existing in the system (e.g. Frankel-Kontorova model). Recently, we have demonstrated analytically and numerically that similar resonant mechanisms also exist in periodically disordered granular chains with no pre-compression. Moreover, these mechanisms are responsible for the aforementioned phenomena of intensive pulse attenuation as well as speeding up of solitary waves in periodic granular chains. In our studies we have considered regular dimer chains consisting of pairs of ‘heavy’ and ‘light’ beads with no pre compression and with elastic Hertzian interaction between beads. A new family of solitary waves was discovered for these systems. These solitary waves may be considered analogous to the solitary wave of a homogeneous chain studied by Nesterenko [1], in the sense that they do not involve separations between beads, but rather satisfy special symmetries or, equivalently resonances in the dynamics. We show that these solitary waves arise from a countable infinity (we conjecture) of nonlinear anti-resonances in the dimer chains. Moreover, solitary waves in the dimers propagate faster than solitary waves in the homogeneous granular chain obtained in the limit of no mass mismatch (i.e., composed of only ‘heavy’ beads). This finding, which might seem to be counter intuitive, indicates that under certain conditions nonlinear anti-resonances can increase the speed of disturbance propagation in disordered granular media, by generating new ways of transferring energy to the far field in these media. Finally, we discuss a contrasting resonance mechanism that leads to the opposite effect, that is, very efficient shock attenuation in the dimer chain. Indeed, we show that under a certain nonlinear resonance condition a granular dimer chain can greatly reduce the amplitude of propagating pulses, through effective scattering of the energy of the pulse to higher frequencies and excitation of alternative intrinsic dynamics of the dimer. This resonance condition may be theoretically predicted and explained, and a very fair correspondence is observed between the analytical solutions and direct numerical simulations. From a practical point of view, these results can have interesting implications in applications where granular media are employed as shock transmitters or attenuators.

Commentary by Dr. Valentin Fuster
2011;():703-712. doi:10.1115/DETC2011-47153.

Safety and robustness will become critical issues when humanoid robots start sharing human environments in the future. In physically interactive human environments, a catastrophic fall is the main threat to safety and smooth operation of humanoid robots, and thus it is critical to explore how to manage an unavoidable fall of humanoids. This paper deals with the problem of reducing the impact damage to a robot associated with a fall. A common approach is to employ damage-resistant design and apply impact-absorbing material to robot limbs, such as the backpack and knee, that are particularly prone to fall related impacts. In this paper, we select the backpack to be the most preferred body segment to experience an impact. We proceed to propose a control strategy that attempts to re-orient the robot during the fall such that it impacts the ground with its backpack. We show that the robot can fall on the backpack even when it starts falling sideways. This is achieved by utilizing dynamic coupling, i.e., by rotating the swing leg aiming to generate spin rotation of the trunk (backpack), and by rotating the trunk backward to drive the trunk to touch down with the backpack. The planning and control algorithms for fall are demonstrated in simulation.

Commentary by Dr. Valentin Fuster
2011;():713-719. doi:10.1115/DETC2011-47407.

The well-recognized Lac repressor protein (LacI) regulates transcription by bending DNA into a loop. In addition to the known role of DNA flexibility, there is accumulating evidence suggesting that the flexibility of LacI also plays a role in this gene regulation. Here we extend our elastic rod model for DNA (previously used to model DNA only) to represent LacI. Specifically, we represent sites of concentrated flexibility in the protein with flexible elastic rod domains; and we represent relatively rigid domains of the protein with stiff elastic rod domains. Our analysis shows the sensitivity of looping energetics to the degree of flexibility within the protein over a large range of DNA lengths. In addition, we show that the predicted energetically dominant binding topology (A ) remains upon introducing protein flexibility.

Topics: DNA
Commentary by Dr. Valentin Fuster
2011;():721-730. doi:10.1115/DETC2011-47887.

The effects of the dynamic excitation on the practical stability of mechanical systems are investigated with reference to an archetypal model which permits to highlight the main ideas without spurious mechanical complexities. First, the effects of the excitation on periodic solutions are analyzed, focusing on bifurcations entailing their disappearance. Then, attractor robustness (i.e., large magnitude of the safe basin) is shown to be necessary but not sufficient to have global safety under dynamic excitation. In fact, the excitation strongly modifies the topology of the safe basins, and a dynamical integrity perspective accounting for the magnitude of the solely compact part of the safe basin must be considered. By means of extensive numerical simulations, robustness/erosion profiles of dynamic solutions/basins for varying axial load and dynamic amplitude are built, respectively. These curves permit to appreciate the practical reduction of system load carrying capacity and, upon choosing the value of residual integrity admissible for engineering design, the practical stability. Dwelling on the effects of the interaction between axial load and lateral dynamic excitation, this paper highlights the fundamental role played by global dynamics as regards a reliable estimation of the practical stability of mechanical systems.

Topics: Stability
Commentary by Dr. Valentin Fuster
2011;():731-737. doi:10.1115/DETC2011-47975.

A nonlinear system identification technique exploiting the dynamic response features of fully nonlinear physics-based plate models extracted by Higher-Order Spectral (HOS) analysis tools is developed. The changes induced by an imperfection in the dynamics through the structural nonlinearities are used as key detection mechanism. The differences in dynamic response of a baseline and a modified/imperfect structure are enhanced by the local nonlinearities induced by the structural modification which thus represent the specific objective of identification. The validation of the procedure and the developed algorithms is carried out through extensive experimental testing employing various plates, including isotropic and composite lay-ups, and excitation sources, including White Gaussian Noise and a train of impulses.

Commentary by Dr. Valentin Fuster
2011;():739-748. doi:10.1115/DETC2011-48006.

Vehicle occupants are sensitive to low frequency vibrations, and these can affect ride-quality and dynamic comfort. Static comfort, a function of the support provided by the seat, is also important. The transmission of vibration to seated occupants and the support provided by the seat can be controlled by appropriately designing the seats. Optimization of seat design requires accurate models of seat-occupant systems can be used to predict both static settling points and the low frequency dynamic behavior of the occupant around those points. A key element in the seat, which is a challenge to model, is the flexible polyurethane foam in the seat cushion. It is a nonlinear, viscoelastic material exhibiting multiple time-scale behavior. In this work, the static and the low-frequency dynamic response of the occupant is examined through a planar multi-body seat-occupant model, which also incorporates a model of flexible polyurethane foam developed from relatively slow cyclic compression tests. This model also incorporates profiles of the seat and the occupant, and includes relatively simple friction models at the various occupant-seat interfaces. The settling point, the natural frequencies, the deflection shapes of the occupant at particular frequencies, and the dynamic force distribution between the seat and the occupant are examined. The effects of seat foam properties on the responses as well as those of including a flexible seat-back frame are also investigated.

Commentary by Dr. Valentin Fuster
2011;():749-758. doi:10.1115/DETC2011-48352.

Effective health diagnosis provides multifarious benefits such as improved safety, improved reliability and reduced costs for the operation and maintenance of complex engineered systems. This paper presents a novel multi-sensor health diagnosis method using Deep Belief Networks (DBN) based state classification. The DBN has recently become a popular approach in machine learning for its promised advantages such as fast inference and the ability to encode richer and higher order network structures. The DBN employs a hierarchical structure with multiple stacked Restricted Boltzmann Machines and works through a layer by layer successive learning process. The proposed multi-sensor health diagnosis methodology using the DBN based state classification can be structured in three consecutive stages: first, defining health states and collecting sensory data for DBN training and testing; second, developing DBN based classification models for the diagnosis of predefined health states; third, validating DBN classification models with testing sensory dataset. The performance of health diagnostics using DBN based health state classification is compared with four existing classification methods and demonstrated with two case studies.

Commentary by Dr. Valentin Fuster
2011;():759-770. doi:10.1115/DETC2011-48386.

This paper presents an efficient algorithm for the simulation of multi-flexible-body systems undergoing discontinuous changes in model definition. The equations governing the dynamics of the transitions from a higher to a lower fidelity model and vice versa are formulated through imposing/removing certain constraints on/from the system. Furthermore, the issue of the non-uniqueness of the results associated with the transition from a lower to a higher fidelity model is dealt with as an optimization problem. This optimization problem is subjected to the satisfaction of the impulse-momentum equations. The divide and conquer algorithm (DCA) is applied to formulate the dynamics of the transition. The DCA formulation in its basic form is time optimal and results in linear and logarithmic complexity when implemented in serial and parallel, respectively. As such, it reduces the computational cost of formulating and solving the optimization problem in the transitions to the finer models. Necessary mathematics for the algorithm implementation is developed and a numerical example is given to validate the method.

Commentary by Dr. Valentin Fuster
2011;():771-778. doi:10.1115/DETC2011-48583.

Molecular replacement (MR) is frequently used to obtain phase information for a unit cell packed with a macromolecule of unknown structure. The goal of MR searches is to place a homologous/similar molecule in the unit cell so as to maximize the correlation with x-ray diffraction data. MR software packages typically perform rotation and translation searches separately. This works quite well for single-domain proteins. However, for multi-domain structures and complexes, computational requirements can become prohibitive and the desired peaks can become hidden in a noisy landscape. The main contribution of our approach is that computationally expensive MR searches in continuous configuration space are replaced by a search on a relatively small discrete set of candidate packing arrangements of a multi-rigid-body model. These candidate arrangements are generated by collision detections on a coarse grid in the configuration space first. The list of feasible arrangements is short because packing constraints together with unit cell symmetry and geometry impose strong constraints. After computing Patterson correlations of the collision-free arrangements, an even shorter list can be obtained using the 10 candidates with highest correlations. In numerical trials, we found that a candidate from the feasible set is usually similar to the arrangement of the target structure within the unit cell. To further improve the accuracy, a Rapidly-exploring Random Tree (RRT) can be applied in the neighborhood of this packing arrangement. Our approach is demonstrated with multi-domain models in silico for 3D, with ellipsoids representing both the domains of the model and target structures. Configurations are defined by sets of angles between the ellipsoids. Our results show that an approximate configuration can be found with mean absolute error (MAE) less than 5 degrees.

Commentary by Dr. Valentin Fuster
2011;():779-785. doi:10.1115/DETC2011-48664.

Legged locomotion of robotic systems on natural or man-made terrain is a complex, hybrid dynamics phenomenon. Effective design and control of these robots requires mathematical understanding of the system dynamics and exploration over a large design space for feasible design solutions. We are working on the development of a high-fidelity, multi-resolution mathematical modeling infrastructure to study the mechanics of legged locomotion. In this paper, we report some of the recent developments made in our effort. We report the implementation of (i) a multi-rigid body dynamics simulator based on cutting edge algorithms in computational multibody dynamics, (ii) a visualization engine that integrates with the dynamics simulator for real-time visualization of the CAD parts of generic multibody systems, (iii) integration and functionality of the coupled entity of the dynamics simulator and the visualization engine as a stand alone application and (iv) our investigations into massively parallel granular media modeling for ab-initio modeling of the contact mechanics of mobility platforms interacting with natural terrain.

Commentary by Dr. Valentin Fuster
2011;():787-793. doi:10.1115/DETC2011-48673.

A computational framework is proposed to path follow the periodic solutions of nonlinear spatially continuous systems and more general coupled multiphysics problems represented by systems of partial differential equations with time-dependent excitations. The set of PDEs is cast in first order differential form (in time) u̇ = f (u ,s,t;c ) where u (s,t) is the vector collecting all state variables including the velocities/time rates, s is a space coordinate (here, one-dimensional systems are considered without lack of generality for the space dependence) and t denotes time. The vector field f depends, in general, not only on the classical state variables (such as positions and velocities) but also on the space gradients of the leading unknowns. The space gradients are introduced as part of the state variables. This is justified by the mathematical and computational requirements on the continuity in space up to the proper differential order of the space gradients associated with the unknown position vector field. The path following procedure employs, for the computation of the periodic solutions, only the evaluation of the vector field f . This part of the path following procedure within the proposed combined scheme was formerly implemented by Dankowicz and coworkers in a MATLAB software package called COCO. The here proposed procedure seeks to discretize the space dependence of the variables using finite elements based on Lagrangian polynomials which leads to a discrete form of the vector field f . A concurrent bifurcation analysis is carried out by calculating the eigenvalues of the monodromy matrix. A hinged-hinged nonlinear beam subject to a primary-resonance harmonic transverse load or to a parametric-resonance horizontal end displacement is considered as a case study. Some primary-resonance frequency-response curves are calculated along with their stability to assess the convergence of the discretization scheme. The frequency-response curves are shown to be in close agreement with those calculated by direct integration of the PDEs through the FE software called COMSOL Multiphysics. Besides primary-resonance direct forcing conditions, also parametric forcing causing the principal parametric resonance of the lowest two bending modes is considered through construction of the associated transition curves. The proposed approach integrates algorithms from the finite element and bifurcation domains thus enabling an accurate and effective unfolding of the bifurcation and post-bifurcation scenarios of nonautonomous PDEs with the underlying structures.

Commentary by Dr. Valentin Fuster
2011;():795-803. doi:10.1115/DETC2011-48711.

A single DNA molecule is a long and flexible biopolymer that contains the genetic code. Building upon the discovery of the iconic double helix over 50 years ago, subsequent studies have emphasized how its biological function is related to the mechanical properties of the molecule. A remarkable system which high-lights the role of DNA bending and twisting is the packing and ejection of DNA into and from viral capsids. A recent 3D reconstruction of bacteriophage φ29 reveals a novel toroidal structure thought to be 30–40 bp of highly bent/twisted DNA contained in a small cavity below the capsid. Here, we extend an elastic rod model for DNA to enable simulation of the toroid as it is compacted and subsequently ejected from a small volume. We compute biologically-realistic forces required to form the toroid and predict ejection times of several nanoseconds.

Topics: Cavities , DNA
Commentary by Dr. Valentin Fuster
2011;():805-812. doi:10.1115/DETC2011-48770.

In 1997 and 2004, small wheeled robots (“rovers”) landed on the surface of Mars to conduct scientific experiments focused on understanding the planet’s climate history, surface geology, and potential for past or present life. Recently, the Mars Exploration Rover (MER) “Spirit” became deeply embedded in regolith at a site called Troy, ending its mission as a mobile science platform. The difficulty faced in navigating mobile robots over sloped, rocky, and deformable terrain has highlighted the importance of developing accurate simulation tools for use in a predictive mobility modeling capacity. These simulation tools require accurate knowledge of terrain model parameters. This paper describes a terramechanics-based tool for simulation of rover mobility. It also describes ongoing work toward estimation of terrain parameters of Mars soil.

Commentary by Dr. Valentin Fuster
2011;():813-821. doi:10.1115/DETC2011-48901.

This paper addresses the study of the nonlinear dynamics of non-smooth systems representative of beams with breathing cracks. The aim is to use the nonlinear characteristics of the system response to identify the damage in cracked structures that behave similarly to bilinear systems and hence exhibit nonlinear phenomena in the dynamic response even for low damage levels. The idea is supported by the study of a piecewise smooth 2-DOF model where a wide variety of nonlinear phenomena has been evidenced, which include among others the bifurcations of super-abundant modes and a number of resonances greater than the system degrees of freedom. All these phenomena are strongly dependent on the stiffness discontinuity which is governed by the damage parameter. A novel method able to detect crack severity and position through measurements of the system nonlinear response has been developed and a cantilever beam with a breathing crack is considered as a numerical test case. The inverse procedure is tested by identifying the position and depth of a crack using pseudo-experimental data; the results show a strong robustness of the method even in the case when the data are affected by measurement errors.

Commentary by Dr. Valentin Fuster
2011;():823-828. doi:10.1115/DETC2011-47473.

The characterization of chaos as a random-like response from a deterministic dynamical system with an extreme sensitivity to initial conditions is well-established, and has provided a stimulus to research in nonlinear dynamical systems in general. In a formal sense, the computation of the Lyapunov Exponent spectrum establishes a quantitative measure, with at least one positive Lyapunov Exponent (and generally bounded motion) indicating a local exponential divergence of adjacent trajectories. However, although the extraction of Lyapunov Exponents can be accomplished with (necessarily noisy) experimental data, this is still a relatively data-intensive and sensitive endeavor. We present here an alternative, pragmatic approach to identifying chaos as a function of system parameters using response frequency characteristics and extending the concept of the spectrogram.

Topics: Chaos
Commentary by Dr. Valentin Fuster
2011;():829-838. doi:10.1115/DETC2011-47949.

The dynamics of drill strings, which are long structures used in drilling operations, are explored numerically and experimentally within this article. A reduced-order distributed parameter model that allows for coupled bending and torsional motions is presented along with forces that take into account interactions between the drill string and the wellbore. Further, a scaled experimental apparatus is presented along with results. Both experimental results and model predictions show backward whirling. Stick-slip interactions are investigated numerically, and the simulation results are seen to be in good agreement with experimental observations. These results could prove useful when designing control schemes for mitigating undesirable torsional and bending motions.

Commentary by Dr. Valentin Fuster
2011;():839-845. doi:10.1115/DETC2011-47950.

We examine analytically and experimentally a new phenomenon of ‘continuous resonance scattering’ in an impulsively excited, two-mass oscillating system. This system consists of a grounded damped linear oscillator with a light, strongly nonlinear attachment. Previous numerical simulations revealed that for certain levels of initial excitation, the system engages in a special type of response that appears to track a solution branch formed by the so-called ‘impulsive orbits’ of this system. By this term we denote the periodic (under conditions of resonance) or quasi-periodic (under conditions of non-resonance) responses of the system when a single impulse is applied to the linear oscillator with the system being initially at rest. By varying the magnitude of the impulse we obtain a manifold of impulsive orbits in the frequency-energy plane. It appears that the considered damped system is capable of entering into a state of continuous resonance scattering, whereby it tracks the impulsive orbit manifold with decreasing energy. Through analytical treatment of the equations of motion, a direct relationship is established between the frequency of the nonlinear attachment and the amplitude of the linear oscillator response, and a prediction of the system response during continuous scattering resonance is provided. Experimental results confirm the analytical predictions.

Commentary by Dr. Valentin Fuster
2011;():847-854. doi:10.1115/DETC2011-48271.

Experimental results are presented on effects of a concentrated mass on chaotic vibrations of a clamped circular plate. The plate has initial deformation due to initial deflection and initial in-plane compressive constraint at the boundary. The concentrated mass is attached on the center of the plate. Under periodic excitation, non-periodic responses with dynamic snap-through are generated on the plates. The responses are inspected by the Fourier spectrum, the Poincaré projection, the maximum Lyapunov exponents and the principal component analysis. The non-periodic responses are found to be chaotic responses. The lowest mode of vibration shows the largest contribution ratio. When the concentrated mass is attached on the plate, the region of the response is shifted to the lower frequency. Furthermore, the width of the frequency region is decreased. The contribution ratio of the lowest mode slightly increases.

Commentary by Dr. Valentin Fuster
2011;():855-859. doi:10.1115/DETC2011-48815.

The bifurcation phenomena produced in a double pendulum under high-frequency horizontal excitation are theoretically and experimentally examined. It has been well known as dynamic stabilization phenomenon that vertical high-frequency excitation can stabilize inverted pendulum. The phenomenon is produced through a sub-critical pitchfork bifurcation. On the other hand, under horizontal high-frequency excitation, the pendulum undergoes a supercritical pitchfork bifurcation and is swung up from the downward vertical position. There have so far been many researches on such dynamics of a single pendulum under the vertical and horizontal high-frequency excitations, but few investigations on multi-degrees-of-freedom system. Also, the utilization of these bifurcations phenomena under the high-frequency excitation is proposed for motion control of underactuated manipulators, but most researches on application is confined to a single pendulum to which a free of two-link underactuated manipulator corresponds. In this paper, toward the development of a three-link underactuated manipulator, we deal with a double pendulum to which two free links of the three-link underactuated manipulator correspond, and theoretically and experimentally investigate bifurcation phenomena in the two pendulums. First, we theoretically predict two pitchfork bifurcation points while increasing the excitation frequency by linear amplitude equations derived using the method of multiple scales. Furthermore, we experimentally examine the swing-up of the pendulums after the first pitchfork bifurcation point and observe that the system has the four types of stable configurations beyond the second pitchfork bifurcation point.

Commentary by Dr. Valentin Fuster
2011;():861-871. doi:10.1115/DETC2011-47168.

This paper examines the limitations of using B-spline representation as an analysis tool by comparing its geometry with the nonlinear finite element absolute nodal coordinate formulation (ANCF) geometry. It is shown that while both B-spline and ANCF geometries can be used to model non-structural discontinuities using linear connectivity conditions, there are fundamental differences between B-spline and ANCF geometries. First, while B-spline geometry can always be converted to ANCF geometry, the converse is not true; that is, ANCF geometry cannot always be converted to B-spline geometry. Second, because of the rigid structure of the B-spline recurrence formula, there are restrictions on the order of the parameters and basis functions used in the polynomial interpolation; this in turn can lead to models that have significantly larger number of degrees of freedom as compared to those obtained using ANCF geometry. Third, in addition to the known fact that B-spline does not allow for straight forward modeling of T-junctions, B-spline representation cannot be used in a straight forward manner to model structural discontinuities. It is shown in this investigation that ANCF geometric description can be used to develop new spatial chain models governed by linear connectivity conditions which can be applied at a preprocessing stage allowing for an efficient elimination of the dependent variables. The modes of the deformations at the definition points of the joints that allow for rigid body rotations between ANCF finite elements are discussed. The use of the linear connectivity conditions with ANCF spatial finite elements leads to a constant inertia matrix and zero Coriolis and centrifugal forces. The fully parameterized structural ANCF finite elements used in this study allow for the deformation of the cross section and capture the coupling between this deformation and the stretch and bending. A new chain model that employs different degrees of continuity for different coordinates at the joint definition points is developed in this investigation. In the case of cubic polynomial approximation, C1 continuity conditions are used for the coordinate line along the joint axis; while C0 continuity conditions are used for the other coordinate lines. This allows for having arbitrary large rigid body rotation about the axis of the joint that connects two flexible links. Numerical examples are presented in order to demonstrate the use of the formulations developed in this paper.

Commentary by Dr. Valentin Fuster
2011;():873-881. doi:10.1115/DETC2011-47187.

This paper introduces a novel model reduction technique, namely Sub-System Global Modal Parameterization (SS-GMP), for real-time simulation of flexible multibody systems. In the past, other system-level model reduction techniques have been proposed for this purpose, but these were limited in applicability due to the large storage requirements for systems with many rigid degrees-of-freedom (DOFs). However, in the SS-GMP approach, the motion of a mechanism is split up into a global motion and a relative motion of the (sub-)system. The relative motion is then reduced according to the Global Modal Parameterization, which is a model reduction procedure suitable for closed chain flexible multibody systems. In combination with suitable explicit solvers, the SS-GMP approach enables (hard) real-time simulations due to the strong reduction in the number of DOFs and the conversion of a system of differential-algebraic equations into a system of ordinary differential equations. The proposed approach is validated numerically with a quarter-car model. This fully flexible mechanism is simulated faster than real-time on a regular PC with the SS-GMP approach while providing accurate results.

Commentary by Dr. Valentin Fuster
2011;():883-888. doi:10.1115/DETC2011-47246.

In this study, the transient analysis of a cable unwinding from a cylindrical spool package is first studied and compared to experiment. Then, a steady-state solution is also compared to transient solution. Cables are assumed to be withdrawn with a constant velocity through a fixed point which is located along the axis of the package. When the cable is flown out of the package, several dynamic forces, such as inertial force, Coriolis force, centrifugal force, tensile force, and fluid-resistance force are acting on the cable. Consequently, the cable becomes to undergo very nonlinear and complex unwinding behavior which is called unwinding balloon. In this paper, to prevent the problems during unwinding such as tangling or cutting, unwinding behaviors of cables in transient state were derived and analyzed. First of all, the governing equations of motion of cables unwinding from a cylindrical spool package were systematically derived using the extended Hamilton’s principles of an open system in which mass is transported at each boundary. And the modified finite difference methods are suggested to solve the derived nonlinear partial differential equations. Time responses of unwinding cables are calculated using Newmark time integration methods. The transient solution is compared to physical experiment, and then the steady-state solution is compared to transient solution.

Commentary by Dr. Valentin Fuster
2011;():889-897. doi:10.1115/DETC2011-47349.

In this investigation, comparison of finite element solutions obtained using the B-spline approach and the absolute nodal coordinate formulation (ANCF) is performed. Furthermore, equivalence of the two formulations with different orders of polynomials and degrees of continuity is demonstrated by several numerical examples. The degree of continuity can be easily controlled in B-spline elements by changing knot multiplicities, while continuity conditions associated with higher order derivatives need to be imposed to achieve C2 and higher continuities in ANCF elements. In order to compare element performances of the third and quartic B-spline and ANCF elements, the three-node quartic ANCF beam element is developed. It is demonstrated in several numerical examples that use of B-spline and ANCF elements with same orders and continuities leads to identical results. Furthermore, effects of polynomial orders and continuities on the accuracy and numerical convergence are demonstrated.

Commentary by Dr. Valentin Fuster
2011;():899-908. doi:10.1115/DETC2011-47442.

The production sector aims towards increasing capacity and energy efficiency. A possibility to achieve this is the usage of manipulators built of lightweight structures in order to raise the maximum velocity, acceleration and payload. This leads to an elastic robot that tends to vibrate. The main focus of this paper is the modeling of a fast moving, elastic robot with three linear axes. These axes are connected by four flexible links driven by synchronous motors with elastic gear racks and bearing elasticities. The Projection Equation in subsystem form is used to calculate the dynamic model. This equation in combination with a Ritz approximation for the flexible links, which are modeled as Rayleigh beams, leads to a set of highly nonlinear ordinary differential equations. The usage of the Projection Equation in subsystem form simplifies the modeling of this system and offers the possibility of a fast numerical integration supported by the Maple ® packages SimCode 2, SimSubs and SimRecursive . The subsystems of the elastic bodies are assembled by the kinematical chain. This leads to the possibility to evaluate the minimal accelerations of the system by a recursive scheme with O(n) efficiency. These results for the endpoint (position and acceleration) of the complete elastically modeled robot are compared to experimental measurements.

Topics: Robots , Modeling
Commentary by Dr. Valentin Fuster
2011;():909-917. doi:10.1115/DETC2011-47732.

A three-dimensional nonlinear finite element for thin beams is proposed within the absolute nodal coordinate formulation (ANCF). The deformation of the element is described by means of displacement vector, axial slope and axial rotation parameter per node. The element is based on the Bernoulli-Euler theory and can undergo coupled axial extension, bending and torsion in the large deformation case. Singularities — which are typically caused by such parameterizations — are overcome by a director per element node. Once the directors are properly defined, a cross sectional frame is defined at any point of the beam axis. Since the director is updated during computation, no singularities occur. The proposed element is a three-dimensional ANCF Bernoulli-Euler beam element free of singularities and without transverse slope vectors. Detailed convergence analysis by means of various numerical examples and comparison to analytical solutions shows the performance and accuracy of the element.

Commentary by Dr. Valentin Fuster
2011;():919-924. doi:10.1115/DETC2011-47794.

In this study, a new approach for generating beam and plate finite elements is proposed for a large-deformation and large-rotation dynamical multibody simulation of thin structures. The elements employ curvatures and/or torsions in the definition of generalized coordinates. This definition of element degrees of freedom is based on intrinsic properties of a spatial curve or a surface and it avoids longitudinal elongations of the beams and plates with associated high frequency vibrations, which helps to avoid problems during numerical simulation.

Commentary by Dr. Valentin Fuster
2011;():925-932. doi:10.1115/DETC2011-47797.

In the past decade, Absolute Nodal Coordinate Formulation (ANCF), which is kind of a finite element method, has been developed for flexible multibody systems with large deformation and large rotation. Almost all studies for ANCF are dedicated to the development of expression ability of flexible multibody system’s behaviors, for example, a study of expansion of ANCF to three dimensional beam, the improvement of computational performance for numerical analysis and so on. On the other hand, there are few studies which extract controllers from the mathematical expressions derived by ANCF. The main aim of this study is to propose a controller design procedure by the use of the mathematical expression which is derived by ANCF. A flexible beam is introduced as a controlled object and the control torque is applied to the one end of the beam. Control objective is to rotate the beam to the desired position and suppress the residual vibration of the beam. In order to derive the mathematical expression for controller design, a kind of ANCF which uses continuum mechanics approach is employed. It is shown that some assumptions and manipulations of the mathematical expression derived by that method result in the linear equation of motion with some uncertainties and the resultant equation has a form suitable for controller design based on μ synthesis framework which is one of the robust control design method. Using μ synthesis framework, controllers are derived for some design parameters and the derived controllers are applied to the controlled object. The validity of the procedure for controller design is shown by numerical simulations and the possibilities and future works of the proposed controller design procedure by the use of mathematical expression by ANCF is discussed.

Commentary by Dr. Valentin Fuster
2011;():933-942. doi:10.1115/DETC2011-47800.

The floating frame of reference formulation (FFRF) together with modal reduction is a standard method in multibody system dynamics. As an advantage of the FFRF, fully nonlinear coupling of small flexible deformations superimposed to arbitrarily large rigid body motion is considered. The idea of the present paper is to apply the FFRF with component mode synthesis to an electromagnetically levitated high-speed rotor, in which large tilting angles may occur, which are not accounted for in classical rotor dynamics. The applicability of FFRF to rotor dynamics, especially close to bending resonance, is not studied in detail in the literature. Thus, fully nonlinear and transient finite element computations are compared to different FFRF-based simulations. In exhaustive numerical studies of a flexible two-disc rotor, comparing FFRF and fully nonlinear transient computations, it is shown that the choice of reference frames and the rotation parameterization influence accuracy of results and CPU-performance.

Commentary by Dr. Valentin Fuster
2011;():943-952. doi:10.1115/DETC2011-47826.

A standard technique to reduce the system size of flexible multibody systems is the component mode synthesis. Selected mode shapes are used to approximate the flexible deformation of each single body numerically. Conventionally, the (small) flexible deformation is added relatively to a body-local reference frame, which results in the floating frame of reference formulation (FFRF). The coupling between large rigid body motion and small relative deformation is nonlinear, which leads to computationally expensive non-constant mass matrices and quadratic velocity vectors. In the present work, the total (absolute) displacements are directly approximated by means of mode shapes, without a splitting into rigid body motion and superimposed flexible deformation. As the main advantage of the proposed method, the mass matrix is constant, the quadratic velocity vector vanishes and the stiffness matrix is a co-rotated constant matrix. Numerical experiments show the equivalence of the proposed method to the FFRF approach.

Commentary by Dr. Valentin Fuster
2011;():953-962. doi:10.1115/DETC2011-47967.

Assumed mode shape method (AMM) has been widely used to derive finite degree-of-freedom (DOF) dynamic model for flexible link manipulators, which theoretically have infinite DOF dynamics. For single flexible manipulator, this approximation changes locations of the zeros of transfer function, between base torque and end-effector displacement. The change in locations of zeros considerably affects accuracy of the model and hence the performance of model-based controllers. This paper presents a comprehensive study on the change in location of zeros due to the truncation associated with AMM. It is shown that the locations of zeros of AMM model depend on four non-dimensional parameters while the locations of the analytical model depend on only two non-dimensional parameters; AMM zeros are obtained from AMM model while analytical zeros derived from infinite order model. A thorough study on the differences between AMM zeros and analytical zeros versus number of mode shapes as well as all the physical parameters is performed. Moreover, guidelines are provided to select the numbers of mode shapes such that the AMM zeros become close to the analytical zeros. These guidelines can easily be used by control engineers and thus makes them valuable for modeling and control of flexible robot manipulators.

Commentary by Dr. Valentin Fuster
2011;():963-970. doi:10.1115/DETC2011-48021.

This paper presents an improved formulation of axial elastic force in three-dimensional Bernoulli-Euler beam element based on the absolute nodal coordinate formulation. An accurate measure of mean axial strain for evaluating the axial elastic forces characterizes the presented formulation. The presented formulation evaluates the mean axial strain accurately by calculating the length of deformed beam element along its neutral axis. A comparison of the conventional formulations of the axial elastic force and the presented formulation is performed in some numerical examples which contain large bending deformation of flexible beam. As a result, it is verified that the presented formulation can express large deformation accurately with smaller number of elements than the conventional formulation which calculates the mean axial strain with straight-line distance between both element nodes. Moreover, it is also verified that the presented formulation can avoid excessive increase in computing time to simulate the dynamic behavior of flexible beam.

Topics: Force
Commentary by Dr. Valentin Fuster
2011;():971-980. doi:10.1115/DETC2011-48548.

Whereas the use of compliant mechanisms is favorable for high precision applications, the constraints must be dealt with carefully. In an overconstrained design the actual natural frequencies and stiffnesses can differ considerably from their intended values. For this reason the awareness and possibly the avoidance of an overconstrained condition is important. We have developed a kinematic analysis with which under-constraints and overconstraints can be detected. A finite element based multibody approach is applied which offers a flexible beam element that is particularly suited to model the wire and sheet flexures frequently encountered in compliant mechanisms. For each element a fixed number of independent discrete deformations are defined that are invariant under arbitrary rigid body motions of the element. In the kinematic analysis only deformations associated with low stiffnesses are allowed, whereas the remaining deformations are prescribed zero. A singular value decomposition is used to determine the rank of the Jacobian matrix associated with the dependent nodal coordinates. Column and row rank deficiency indicate an underconstrained and overconstrained system, respectively. For an overconstrained system a statically indeterminate stress distribution can be derived from the left singular matrix. In this way the overconstraints can be visualized clearly as is illustrated with examples of compliant straight guidance mechanisms. The possible solutions to eliminate the overconstraints are found easily from the visualization.

Commentary by Dr. Valentin Fuster
2011;():981-990. doi:10.1115/DETC2011-48709.

Dynamic modeling of a flexible hub-beam system with an eccentric tip mass including nonlinear hysteretic contact is studied in this paper. In reality, the model is intended to represent the mechanical finger of an actuator for a piano key. Developing a device to achieve a desired finger-key contact force profile that realistically replicates that of a real pianist’s finger is the main objective of this research. The proposed actuation system consists of a flexible arm which is attached to a DC brushless rotary motor thorough a hub. The compliant arm behaves as a cantilever beam to which an eccentric tip mass has been attached at its free end. During the piano key stroke, the contact force input from the tip causes the key to rotate and impact the ground through an interface lined with stiff felt to suppress vibrations and noise. Euler-Bernoulli beam theory in conjunction with Lagrange’s method is utilized to obtain the governing equations of motion for the system. The finite element method is used as the discretization procedure for the flexible cantilever beam, which can be considered a distributed parameter system. To include contact dynamics at the stop, the nonlinear hysteretic behavior of felt under compression is modeled in such a way that smooth transitions between loading and unloading stages are produced, thus ensuring accurate response under dynamic conditions, and particularly with partial loading and unloading states that occur during the contact period. Simulation results show excessive vibration is produced due to the arm flexibility and also the rigid-body oscillations of the arm, especially during the period of key-felt contact. To eliminate these vibrations, the system was supplemented with various dashpot models, including a simple grounded rotational dashpot, and a grounded rotational dashpot with a one-sided relation. The results of simulations are presented showing the effect on vibration behavior attributed to these additional components.

Commentary by Dr. Valentin Fuster
2011;():991-998. doi:10.1115/DETC2011-48816.

This contribution discusses how a flexible body formalism, specifically, the Absolute Nodal Coordinate Formulation (ANCF), is combined with a frictional/contact model using the Discrete Element Method (DEM) to address many-body dynamics problems; i.e., problems with hundreds of thousands of rigid and deformable bodies. Since the computational effort associated with these problems is significant, the analytical framework is implemented to leverage the computational power available on today’s commodity Graphical Processing Unit (GPU) cards. The code developed is validated against ANSYS and FEAP results. The resulting simulation capability is demonstrated in conjunction with hair simulation.

Topics: Simulation
Commentary by Dr. Valentin Fuster
2011;():999-1008. doi:10.1115/DETC2011-47723.

A research paradox currently lies in the design of miniaturized vibratory energy harvesters capable of harnessing energy efficiently from low-frequency excitations. To address this problem, this effort investigates the prospect of utilizing super-harmonic resonances of a bi-stable system to harvest energy from excitation sources with low-frequency components. Towards that objective, the paper considers the electromechanical response of an axially-loaded clamped-clamped piezoelectric beam harvester with bi-stable potential characteristics. By numerically constructing the voltage-frequency bifurcation maps of the response near the super-harmonic resonance of order two, it is shown that, for certain base excitation levels, the harvester can exhibit responses that are favorable for energy harvesting. These include a unique branch of large-orbit periodic inter-well oscillations, coexisting branches of large-orbit solutions, and a bandwidth of frequencies where a unique chaotic attractor exists. In these regions, the harvester can produce power levels that are comparable to those obtained near the primary resonance.

Commentary by Dr. Valentin Fuster
2011;():1009-1019. doi:10.1115/DETC2011-47833.

In two recent studies [1; 2], the authors have presented the concept and the analytical modeling framework for a scalable wind micro-power generator. The device transforms wind energy into electricity via the self-excited oscillations of a piezoelectric reed embedded within a cavity. Based on the model developed in [2], this effort utilizes the Routh-Hurwitz criterion and numerical algorithms to understand the influence of the design parameters on the device’s response with the goal of minimizing the cut-on wind speed and maximizing the output power. Results indicate that, for a beam of certain design parameters, there exists an optimal chamber volume that minimizes the cut-on wind speed of the device. This optimal volume is inversely proportional to the beam’s first modal frequency. Results also indicate that the cut-on wind speed can be decreased significantly as the aperture’s width is decreased. However, due to the reduced strain rate in the piezoelectric layer, it is observed that minimizing the cut-on wind speed does not always correspond to an increase in the output power. As such, in an attempt to study the influence of the design parameters on the output power, design charts were constructed to select the optimal design parameters for a known average wind speed. Experimental results are also presented to qualitatively verify the theoretical trends.

Topics: Design , Generators
Commentary by Dr. Valentin Fuster
2011;():1021-1032. doi:10.1115/DETC2011-47968.

This work describes the modeling, analysis, predictive design, and control of self-excited oscillators, and associated arrays, founded upon electromagnetically-actuated microbeams. The study specifically focuses on the characterization of nonlinear behaviors arising in isolated oscillators and small arrays of nearly-identical, mutually-coupled oscillators. The work provides a framework for the exploration of larger oscillator arrays with different forms of coupling and feedback, which can be exploited in practical applications ranging from signal processing to micromechanical neurocomputing.

Commentary by Dr. Valentin Fuster
2011;():1033-1040. doi:10.1115/DETC2011-48253.

Doubly-fed induction generators (DFIGs) are commonly used in variable-speed wind turbines for more power extraction. Unlike previous research on DFIG wind turbines, which typically uses an equivalent lumped mass model of the drive train dynamics, but does not include detailed aerodynamic/mechanical representations, this paper investigates on the modelling and control of DFIG wind turbines by following a systematic approach based on a flexible multibody simulation software. The wind turbine structure, generator and control subsystem models are modularly developed for the S4WT package (Samcef for Wind Turbines), which is a user interface for the analysis of wind turbines. An extension of the finite element method is available in the flexible multibody dynamics solver, for the representation of the non-mechanical components, i.e., the generator and the control system, so that the coupled mechatronic system is simulated in a strongly coupled way. This integrated approach is less intricate and more robust than approaches based on an external DLL or co-simulation methods. The objective of this work is to analyze the control-generator-structure interactions in a wind turbine system. The power optimization control is elaborated in detail. A 2MW DFIG wind turbine prototype model is presented for validation. Dynamic analysis including the control effects and the influence of the structural flexibility is provided in an overall range.

Commentary by Dr. Valentin Fuster
2011;():1041-1047. doi:10.1115/DETC2011-48599.

We consider a chain of N nonlinear resonators with natural frequency ratios of approximately 2:1 along the chain and weak nonlinear coupling of a form that allows energy to flow between resonators. Specifically, the coupling is such that the response of one resonator parametrically excites the next resonator in the chain, and also creates a resonant backaction on the previous resonator in the chain. This class of systems, which is being proposed for micro-electro-mechanical frequency dividers, is shown to have rich dynamical behavior. Of particular interest is the case when the high frequency end of the chain is resonantly excited, and coupling results in the potential for a cascade of sub-harmonic bifurcations down the chain. When the entire chain is activated, that is, when all N resonators have non-zero amplitudes, if the input frequency on the first resonator is Ω , then the terminal resonator responds with frequency Ω /2 N . The details of the activation depend on the strength and frequency of the input, the level of resonator dissipation, and the mistuning in the chain. In this paper we present analytical results, based on perturbation methods, which provide useful predictions about these responses in terms of system and input parameters. Parameter conditions for activation of the entire chain are derived, along with results about other phenomena, such as bistability and partial activation of the chain. We demonstrate the utility of the predictive results by direct comparison with simulations of the equations of motion, and we also present samples of mechanical and electromechanical systems that realize the desired properties. These results will be useful for the design and operation of mechanical frequency dividers based on subharmonic resonances.

Commentary by Dr. Valentin Fuster
2011;():1049-1055. doi:10.1115/DETC2011-47323.

The cables used in cable-stayed bridges are known to have low levels of damping and, as a result, their large amplitude vibrations represent a problem for the structure. Therefore, augmenting the natural damping of cables is used as a strategy to decrease their vibration response. Here we investigate how this precaution changes the dynamics of the cable vibration response. We use a four-mode model of an inclined cable specifically, that is fixed at the top, and vertically excited at the base in order to simulate excitation due to the deck motion. This model simulates the internal resonances between in-plane and out-of-plane modes of vibration. The deck motion is taken to be at a frequency close to the natural frequency of the second cable mode in each plane, hence, directly exciting just the second in-plane mode. The objective of this study is to examine how the regions of stability (of the different possible solutions) change with variations in the modal damping value of the cable. The damping ratios of the cables used for bridges being considered is usually about 0.2% ; here we investigate increasing ξ up to 1% . Three-parameter analysis shows that 2:1 resonance occurs for damping ratios larger than 0.6% ; but it requires higher excitation amplitudes than for damping ratios about 0.2% . The analysis of the damping ratio variation shows us that bifurcations that can lead to sudden change in the cable dynamics still persist for the parameter ranges considered in this study. However, they occur at excitation frequencies that are further from the second natural frequency of the cable.

Topics: Cables , Damping , Vibration
Commentary by Dr. Valentin Fuster
2011;():1057-1065. doi:10.1115/DETC2011-47355.

The nonlinear dynamic behavior of a laminated composite cantilever plate is investigated in this paper. The extended Melnikov method is employed to predict the multi-pulse chaotic motions of the cantilever plate. The model is based on the wing flutter of the airplane. The cantilever plate is considered to be subjected to the in-plane and transversal excitations. The Reddy’s high-order shear deformation theory as well as von Kármán type equations are used to establish the equation of motion for the cantilever plate. Applying the Galerkin procedure to the partial differential governing equations of motion for the system, we obtain equations of transverse displacement. Then the method of multiple scales is used to obtain the averaged equations. Finally, the extended Melnikov method is used to analyze the nonlinear behavior in the cantilever plate system. The theoretical result shows that there exists multi-pulse jumping movement. The numerical results also reveal such chaotic phenomenon.

Commentary by Dr. Valentin Fuster
2011;():1067-1076. doi:10.1115/DETC2011-47406.

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design.

Topics: Resonance , Equations
Commentary by Dr. Valentin Fuster
2011;():1077-1086. doi:10.1115/DETC2011-47452.

With the first major installation in North American railroads during the 1960’s, concrete ties were believed to last longer than timber ties and have the potential for reduced life cycle costs. However, their characteristic response to initial pretension release as well as dynamic track loading is not well understood. In North America, concrete ties have been found vulnerable to rail seat deterioration (RSD), but the mechanisms contributing to RSD failures are not well understood. To improve such understanding, a comprehensive computational study of the tie response to dynamic track forces is needed. This paper presents an initial research effort in this direction that models concrete crossties as heterogeneous media in three-dimensional finite element analyses, i.e., the prestressing strands, concrete matrix and the strand-concrete interfaces are represented explicitly. Damaged plasticity models are employed for the concrete material, and linear elastic bond-slip relations, followed by damage initiation and evolution, are adopted for the strand-concrete interfaces. Further, the ballast is modeled with an Extended Drucker-Prager plasticity model, and the subgrade is modeled as an elastic half space. All material parameters are obtained from the open literature. Currently the rail fastening systems are not included in modeling. Two loading scenarios are simulated: pretension release and direct rail seat loading. The modeling approach is able to predict the deformed tie shape, initial interface deterioration, the compressive stress state in concrete and residual tension in the strands upon pretension release. The transfer lengths of the prestressing strands can be readily calculated from the analysis results. Further predicted are the rail seat force-displacement characteristics and the potential failure mode of a concrete crosstie under direct rail seat loading. The responses of two railroad concrete crossties with 8-strand and 24-wire reinforcements, respectively, are studied using the presented modeling framework. The analyses indicate a potential failure mode of tensile cracking at the tie base below the rail seats. The results show that the 24-wire tie is better able to retain the pretension in the reinforcements than the 8-strand tie, resulting in slightly stronger rail seat force-displacement characteristics and higher failure load. The effects of the load application method and the subgrade modeling on the predicted tie response are further studied.

Commentary by Dr. Valentin Fuster
2011;():1087-1099. doi:10.1115/DETC2011-47549.

This paper discusses and further investigates a new methodology, “Static Modes Switching” (SMS), improving computational efficiency for elastic multibody (EMBS) systems. This method focuses on mechanisms in which loading is possible in many degrees of freedom, but only few of them are simultaneously loaded at a given moment in time (e.g. sliding elements, gear contact, etc.). The methodology adapts during simulation the mode set used to represent component flexibility, by judiciously choosing only those static modes that are contributing actively to the body deformation. First, the general methodology is presented, then the current work and its original contributions are discussed; namely SMS is tested on a 3D mechanism including multiple flexible bodies on which sliding elements are present. Moreover, as opposed to previous studies, the locations where external excitation is acting is not known a priori. Finally, some limitations of the proposed methodology are treated with focus on the numerical discontinuities introduced by the switching of the modal base and their propagation to neighbouring bodies.

Topics: Simulation
Commentary by Dr. Valentin Fuster
2011;():1101-1109. doi:10.1115/DETC2011-47645.

Nowadays, engineers still search for more efficient methods in order to decrease simulation times. However, most simulation environments do not use the full power provided by modern PCs. Even though every modern computer is equipped with a multicore processor, only very few simulation environments use more than one core for simulations. There are various possibilities to parallelize simulations. One approach is to partition the model into several submodels. Using adequate solvers for each submodel can result in lower computation times, especially if there is a significant difference in the time constants of the submodels. Other approaches are based on parallelization of the ODE solver. For example, it is possible to parallelize the linear algebra methods inside the solver. Parallelization of the solver itself is another way to use the multicore architecture. From the modeling and simulation point of view, the latter approach is more interesting. Consequently, the question is whether it is beneficial to partition the model or to use a parallelized solver. In this paper this question is answered at least for an example system. However, the more efficient approach may not be the better approach for the usage inside a simulation environment. Therefore, it is discussed which approach can be automated and integrated easier into a simulation environment.

Commentary by Dr. Valentin Fuster
2011;():1111-1120. doi:10.1115/DETC2011-47876.

The main focus in the presented work is on the sensitivity analysis of the comfort and handling characteristics of a commercial vehicle with Individual Front Suspension (IFS). For the sensitivity analysis, two simulations in frequency domain are conducted: road input and steering input frequency responses. Employing the model of the tractor semitrailer combination for the above mentioned analyses, this study evaluates the influence of five damping coefficients — cab, front and rear axle shock absorbers — on our objectives. The results that are provided in Pareto fronts clearly show the great influence of the studied parameters, particularly the front axle and cab lateral dampers, on the vehicle comfort and handling for the performed simulations. Finally, the model is updated with the chassis and cab lateral damper coefficients to run a simulation on random roads for more detailed comfort examinations. This analysis confirms the obtained improvements in the outcome of the sensitivity study.

Topics: Vehicles
Commentary by Dr. Valentin Fuster
2011;():1121-1130. doi:10.1115/DETC2011-48108.

A large effort in the analysis of a physical system is the development of a model describing its behavior. The non-linear and time variant characteristic of many mechanical systems can be hardly represented by an analytical model without a remarkable increase of its complexity which contrasts with the need to obtain acceptable results in real-time such as in multibody simulations, system control design and Hardware in the loop (HIL ) testing. In this context, the use of artificial neural networks are recognized as a powerful modeling tool to produce accurate model with reduced complexity. On the other hand their response to inputs outside the learning range may lead to unrealistic results. This paper presents an hybrid modeling technique, which combines a physical model with a neural network. The physical model describes the gross behavior of the system and the neural network captures the non-linear non-modeled behaviors or the effect of time-varying parameters. It is also proposed a method to limit the outside-range unpredicted responses. A RC car shock absorber is used as test case. Experimental results show that the neural network improves the physical model output capturing nonlinear aspects such as the hysteresis, the fluid leakage and the increase of its temperature.

Commentary by Dr. Valentin Fuster
2011;():1131-1140. doi:10.1115/DETC2011-48202.

Serial planar manipulators are diffusely used either as stand-alone machines or as part of more complex cells, and many commercial planar manipulators are available on the market. These commercial machines are mainly destined to accomplish low-speed tasks, and they are designed by taking into account their flexibility at most in the joints. Unfortunately, there are particular installation conditions in which even low-speed tasks can generate low-frequency vibrations that highly interfere with the task. This aspect is highlighted here with reference to a commercial 3R planar manipulator, and how to manage this problem is explained. In this sight, a flexible multibody model is developed where the flexibility of the frame, the manipulator is fixed to, is modeled over the flexibility of the joints, that is introduced as lumped stiffness. In particular, the flexible frame is included in the model by using a Component Mode Synthesis methodology, in which only the natural modes of vibration and the static constrain modes are accounted. The model is validated through an experimental campaign. The experimental tests consist of several modal analyses, together with acceleration and laser Doppler measurements in operational conditions. This methodology allows to provide a model which takes into account the installation conditions, and gives a tool for studying ad-hoc solutions which prevent the occurrence of low-frequency vibrations.

Topics: Manipulators
Commentary by Dr. Valentin Fuster
2011;():1141-1150. doi:10.1115/DETC2011-48206.

One of the challenging issues in the area of flexible multibody systems is the ability to properly account for the geometric nonlinear effects that are present in many applications. One common application where these effects play an important role is the dynamic modeling of twist beam axles in car suspensions. The purpose of this paper is to examine the accuracy of the results obtained using four common modeling methods used in such applications. The first method is based on a spline beam approach in which a long beam is represented using piecewise rigid bodies interconnected by beam force elements along a spline curve. The beam force elements use a simple linear beam theory in approximating the forces and torques along the beam central axis. The second approach uses the well known method of component mode synthesis that is based on the linear elastic theory. Using this method the deformation of the beam, which is modeled as one flexible body, is defined using its own vibration and static correction mode shapes. The equations of motion are, in this case, written in terms of the system’s generalized coordinates and modal participation factors. The linear elastic theory is used again in the third approach using a slightly different technique called the sub-structuring synthesis method. This method is based on dividing the flexible component into sub-structures, in which, the method of component mode synthesis is used to describe the deformation of each substructure. The fourth approach is based on a co-simulation technique that uses a Multibody System (MBS) solver and an external nonlinear Finite Element Analysis (FEA) solver. The flexibility of any body in the multibody system is, in this case, modeled in the external nonlinear FEA solver. The latter calculates the forces due to the nonlinear deformations of the flexible body in question and communicates that to the MBS solver at certain attachment points where the flexible body is attached to the rest of the multibody system. The displacements and velocities of these attachment points are calculated by the MBS solver and are communicated back to the nonlinear FEA solver to advance the simulation. The four approaches described are reviewed in this paper and a multibody system model of a car suspension system that includes a twist beam axle is presented. The model is examined four times, once using each approach. The numerical results obtained using the different methods are analyzed and compared.

Commentary by Dr. Valentin Fuster
2011;():1151-1158. doi:10.1115/DETC2011-48234.

For various problems of practical importance, such as disturbance rejection or constrained control, the determination of invariant sets provides insightful information on the influence of unknown bounded signals on the dynamical system behavior. In order to characterize the effect of those signals on the system, the determination of the minimal robust positively invariant (mRPI) set is of great interest. On the other side, the presence of time delays is ubiquitous in process control and it seems natural to use invariant set theory to analyze time delay systems affected by additive disturbance. The present paper deals with computation and characterization of the delay-independent minimal robust positively invariant region in the set-theoretic framework. The Banach fixed point theorem will be used to specify the existence and uniqueness conditions for this set. Here we also provide a procedure for the construction of invariant approximations of this limit set as well as discussion on the efficient computation for practical usage. Supplementary, at the end is pointed out an interesting correlation between proposed results and existence of the mRPI sets for switching dynamics. In this study we are particularly interested in discrete time systems. Outlined results are confirmed by a numerical example.

Topics: Delays
Commentary by Dr. Valentin Fuster
2011;():1159-1170. doi:10.1115/DETC2011-48383.

Generalized divide and conquer algorithm (GDCA) is presented in this paper. In this new formulation, generalized forces appear explicitly in handle equations in addition to the spatial forces, absolute and generalized coordinates which have already been used in the original version of DCA. To accommodate these generalized forces in handle equations, a transformation is presented in this paper which provides an equivalent spatial force as an explicit function of a given generalized force. Each generalized force is then replaced by its equivalent spatial force applied from the appropriate parent body to its child body at the connecting joint without violating the dynamics of the original system. GDCA can be widely used in multibody problems in which a part of the forcing information is provided in generalized format. Herein, the application of the GDCA in controlling multibody systems in which the known generalized forces are fedback to the system is explained. It is also demonstrated that in inverse dynamics and closed-loop control problems in which the imposed constraints are often expressed in terms of generalized coordinates, a set of unknown generalized forces must be considered in the dynamics of system. As such, using both spatial and generalized forces, GDCA can be widely used to model these complicated multibody systems if it is desired to benefit from the computational advantages of the DCA.

Commentary by Dr. Valentin Fuster
2011;():1171-1180. doi:10.1115/DETC2011-48657.

Multibody system with flexible and / or rigid bodies are found in various applications of science and engineering. Many of these systems have topological constraints in the form of kinematically closed loop topologies. Similarly, many of these systems have non-holonomic constraints that are either linear or nonlinear in the system velocities. In this paper, an efficient algorithm is presented for simulating the dynamics of multi-body systems of rigid or flexible bodies in generalized topologies with particular emphasis on treatment of topological and non-holonomic constraints. The flexible bodies are modeled using the small deformation large displacement approach. This algorithm achieve linear and logarithmic complexities in serial and parallel implementation and provides robust performance.

Commentary by Dr. Valentin Fuster
2011;():1181-1190. doi:10.1115/DETC2011-47002.

Nonlinear limit cycle oscillations of an aeroelastic energy harvester are exploited for enhanced piezoelectric power generation from aerodynamic flows. Specifically, a flexible beam with piezoelectric laminates is excited by a uniform axial flow field in a manner analogous to a flapping flag such that the system delivers power to an electrical impedance load. Fluid-structure interaction is modeled by augmenting a system of nonlinear equations for an electroelastic beam with a discretized vortex-lattice potential flow model. Experimental results from a prototype aeroelastic energy harvester are also presented. Root mean square electrical power on the order of 2.5 mW was delivered below the flutter boundary of the test apparatus at a comparatively low wind speed of 27 m/s and a chord normalized limit cycle amplitude of 0.33. Moreover, subcritical limit cycles with chord normalized amplitudes of up to 0.46 were observed. Calculations indicate that the system tested here was able to access over 17% of the flow energy to which it was exposed. Methods for designing aeroelastic energy harvesters by exploiting nonlinear aeroelastic phenomena and potential improvements to existing relevant aerodynamic models are also discussed.

Topics: Cycles
Commentary by Dr. Valentin Fuster
2011;():1191-1200. doi:10.1115/DETC2011-47377.

A number of practical structures such as compliant offshore towers can be physically modeled, as a first approximation, as an inverted pendulum. The nonlinear dynamics of such model can present some complex features due to the nonlinear coupling among its degrees-of-freedom. In this paper a model of a spatial inverted pendulum restrained by three inclined extensional springs is adopted. Geometric imperfections are considered, and the solutions for both perfect and imperfect systems are presented herein. Especial attention is given to the determination of the nonlinear vibration modes. Non-similar and similar NNMs are obtained analytically by direct application of asymptotic methods and the results show important NNM features such as instability and multiplicity of modes. Poincaré maps of the conservative system are used to identify the existence of modes that do not have a linear counterpart. Analytical approximations are derived for these nonlinear modes by the use of a two-dimensional polynomial fitting procedure obtained by the application of the Levenberg-Marquardt method. The points coordinates used in the fitting procedure were obtained through numerical integration of the governing equations of motion. Such analytical expressions can then be used in modal reduction, parametric analysis and in the derivation of important features of the system such as its frequency-amplitude relations and resonance curves.

Topics: Pendulums
Commentary by Dr. Valentin Fuster
2011;():1201-1209. doi:10.1115/DETC2011-47495.

This paper deals with further development of Modified Modal Domain Analysis (MMDA), which is a breakthrough method in the reduced order modeling of a bladed rotor with geometric mistuning. The main focus of this paper is to show that deviations in mass and stiffness matrices due to mistuning, estimated by Taylor series expansions in terms of independent Proper Orthogonal Decomposition variables representing geometric variations of blades, can be used for MMDA. This result has rendered Monte Carlo simulation of the response of a bladed rotor with geometric mistuning to be easy and computationally efficient.

Topics: Modeling , Rotors , Stiffness
Commentary by Dr. Valentin Fuster
2011;():1211-1218. doi:10.1115/DETC2011-47654.

The normal form technique is an established method for analysing weakly nonlinear vibrating systems. It involves applying a simplifying nonlinear transform to the first-order representation of the equations of motion. In this paper we consider the normal form technique applied to a forced nonlinear system with the equations of motion expressed in second-order form. Specifically we consider the selection of the linearised natural frequencies on the accuracy of the normal form prediction of sub- and superharmonic responses. Using the second-order formulation offers specific advantages in terms of modeling lightly damped nonlinear dynamic response. In the second-order version of the normal form, one of the approximations made during the process is to assume that the linear natural frequency for each mode may be replaced with the response frequencies. Here we will show that this step, far from reducing the accuracy of the technique, does not affect the accuracy of the predicted response at the forcing frequency and actually improves the predictions of sub and superharmonic responses. To gain insight into why this is the case, we consider the Duffing oscillator. The results show that the second-order approach gives an intuitive model of the nonlinear dynamic response which can be applied to engineering applications with weakly nonlinear characteristics.

Commentary by Dr. Valentin Fuster
2011;():1219-1226. doi:10.1115/DETC2011-47982.

Aeroelastic instabilities of a panel may result in buckling (divergence) or flutter (Hopf bifurcation), when it is acted upon by induced aerodynamic and externally applied loads under supersonic/hypersonic environment in this paper. These instabilities are stabilized using nonlinear bifurcation control with piezoelectric actuation. The center manifold theory is used to extract subsystems which completely capture the bifurcation behavior of the original system near critical parameter values represented by sets of parametrised first-order differential equations with feedback control. The principle of normal form is used to simplify the nonlinear terms of the lower dimensional systems. The proposed controllers, which employ purely nonlinear state feedback, are used to modify the nonlinear characteristics of the post bifurcation limit sets by setting the amplitudes and rates of growth to the desired values. Numerical results show that the resulting closed-loop systems are effectively stabilized at the neighborhood of critical values.

Topics: Bifurcation
Commentary by Dr. Valentin Fuster
2011;():1227-1239. doi:10.1115/DETC2011-48506.

This study investigates the vibration structure of high-speed, gyroscopic planetary gears. The vibration modes of these systems are complex-valued and speed dependent. Three mode types exist, and these are classified as planet, rotational, and translational modes. Each mode type is mathematically proven by the use of a candidate mode method. Reduced eigenvalue problems are determined for each mode type. The eigenvalues for an example high-speed planetary gear are determined over a wide range of carrier speeds. Divergence and flutter instabilities are observed at extremely high speeds.

Commentary by Dr. Valentin Fuster
2011;():1241-1252. doi:10.1115/DETC2011-48689.

An analytical solution for the nonlinear vibration of gear pairs that exhibit partial and total contact loss is found. The gear teeth can have arbitrary tooth surface modifications. Such modifications and dynamic displacements separate parts of gear tooth surface otherwise designed to be in contact. This is partial contact loss. The excitation and the nonlinearity are not specified but are found from the force-deflection function of the gear pair, which comes from independent analysis, such as a finite element model. Fourier and Taylor series expansions of the force-deflection function capture the flexibility, nonlinearity, and the excitation in a few coefficients. The gear elastic behavior includes Hertz contact, bending, and shear. The nonlinearity arises chiefly from tooth surface modifications due to the dependence of contact upon the instantaneous dynamic mesh force. Although this work focuses on gear pairs with tooth surface modifications, the physical system from which the force-deflection function comes is not limited to gear pairs. Sphere/half-space contact vibrations are also analyzed. The dynamic frequency-amplitude relation at the steady-state is found using the method of multiple scales. Comparisons with experiments from the literature on gear vibrations and sphere/half-space contact vibrations verify the method.

Commentary by Dr. Valentin Fuster
2011;():1253-1260. doi:10.1115/DETC2011-48846.

A time-accurate high-fidelity finite element model for timing belt-drives is presented. The belt is modeled using flexible spatial lumped parameters beam elements. Each finite element belt node can be considered as a rigid body whose contact geometry is used to model the contact surfaces of the belt teeth. The sprockets and pulleys are modeled as rigid bodies. A penalty model is used to impose the joint/contact constraints. An asperity-based friction model is used to model joint/contact friction. A recursive bounding box contact search algorithm is used to allow fast contact detection between contact points on the belt surface (master contact surface) and a polygonal surface representation of the sprockets/pulleys. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The model is partially validated by comparing to a previously published steady-state study where the belt tooth loads over the driven sprocket were experimentally measured. The model can help improve the design of timing belts including increasing the range of operating speeds, reduce the vibrations and noise and increase the drive durability.

Commentary by Dr. Valentin Fuster

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