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Active Control of Viscoelastic Systems by the Method of Receptance

[+] Author Affiliations
Kumar V. Singh, Xiaoxuan Ling

Miami University, Oxford, OH

Paper No. IMECE2016-67725, pp. V04AT05A056; 10 pages
doi:10.1115/IMECE2016-67725
From:
  • ASME 2016 International Mechanical Engineering Congress and Exposition
  • Volume 4A: Dynamics, Vibration, and Control
  • Phoenix, Arizona, USA, November 11–17, 2016
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5054-1
  • Copyright © 2016 by ASME

abstract

Viscoelastic materials both stores and dissipate energies and have frequency and temperature dependent properties and hence by tuning and optimizing their damping (viscous) and stiffness (elastic) properties they can be used as passive controlling devices in wide range of vibration applications. If the control of viscoelastic systems (viscoelastic structures or structures composed of viscoelastic elements) to be realized by active means, then an accurate mathematical modeling of the viscoelastic system is needed. In practice, various material models and approximation techniques such as Biot model, Golla-Hughes-McTavish (GHM) model and Anelastic Displacement Field (ADF) methods are used to model the dynamic behavior of viscoelastic systems. These models are then transformed into approximating state space models which introduces several challenges: (i) they increase the size of the related eigenvalue problems, (ii) state space realization introduces non-physical internal state variables, and, (iii) the feedback control implementation poses practical challenges such as observer and state estimator design. In this research it is shown that the active control for viscoelastic structures can be designed accurately by only utilizing the available transfer functions. These transfer functions can be obtained from dynamic experiments and the active feedback control is designed without having the knowledge of approximated state-space system matrices. The problem associated with the active control for viscoelastic system is formulated as feedback control problems in frequency domain by using the receptance method. Active control for poles and zeros assignment of the viscoelastic systems is demonstrated using numerical examples associated with the multi-degree-degree of freedom systems. It is also shown that a nested active controller can also be designed for continuous structures (beams/rods) supported by viscoelastic elements. It is highlighted that such a controller design requires modest size of transfer functions and solution of the set of linear system of equations.

Copyright © 2016 by ASME

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