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Nonlinear Coupled Transverse and Axial Vibration of Variable Cross-Section Beam Flexures Interconnecting Rigid Body

[+] Author Affiliations
Hasan Malaeke, Hamid Moeenfard

Ferdowsi University of Mashhad, Mashhad, Iran

Amir H. Ghasemi

University of Michigan, Ann Arbor, MI

Paper No. DSCC2016-9881, pp. V001T11A006; 8 pages
  • ASME 2016 Dynamic Systems and Control Conference
  • Volume 1: Advances in Control Design Methods, Nonlinear and Optimal Control, Robotics, and Wind Energy Systems; Aerospace Applications; Assistive and Rehabilitation Robotics; Assistive Robotics; Battery and Oil and Gas Systems; Bioengineering Applications; Biomedical and Neural Systems Modeling, Diagnostics and Healthcare; Control and Monitoring of Vibratory Systems; Diagnostics and Detection; Energy Harvesting; Estimation and Identification; Fuel Cells/Energy Storage; Intelligent Transportation
  • Minneapolis, Minnesota, USA, October 12–14, 2016
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-5069-5
  • Copyright © 2016 by ASME


The objective of this paper is to analytically study the nonlinear behavior of variable cross-section beam flexures interconnecting an eccentric rigid body. Hamilton’s principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. Using a single mode approximation, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. The method of multiple scales are employed to obtain parametric closed-form solutions. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. These analytical expressions provide design insights for modeling and optimization of more complex flexure mechanisms for improved dynamic performances.

Copyright © 2016 by ASME



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