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research-article

Nonsymmetric nonlinear dynamics of piezoelectrically actuated beams

[+] Author and Article Information
Mergen H. Ghayesh

School of Mechanical Engineering Adelaide, South Australia 5005 Australia mergen.ghayesh@adelaide.edu.au

Hamed Farokhi

Faculty of Engineering and Environment Department of Mechanical & Construction Engineering Wynne-Jones Building Room WJ201 Newcastle upon Tyne NE1 8ST, UK Newcastle upon Tyne, UK NE1 8ST United Kingdom hamed.farokhi@northumbria.ac.uk

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received August 14, 2018; final manuscript received May 5, 2019; published online xx xx, xxxx. Assoc. Editor: Mohammed Daqaq.

ASME doi:10.1115/1.4043716 History: Received August 14, 2018; Accepted May 06, 2019

Abstract

The nonlinear behaviour of a piezoelectrically actuated clamped-clamped beam has been examined numerically while highlighting the nonsymmetric response of the system. The nonlinearly coupled electromechanical model of the piezoelectric-beam system is developed employing the Bernoulli-Euler theory along with the piezoelectric stress-voltage equations. A general nonsymmetric configuration is considered with a piezoelectric patch partially covering the beam. The geometric nonlinearities of stretching type are taken into account for both piezoelectric patch and the beam. Through use of the generalised Hamilton's principle, the nonlinearly coupled electromechanical equations of transverse and longitudinal motions of the piezoelectrically actuated beam are derived. A high-dimensional Galerkin scheme is utilised to recast the equations of partial differential type into ordinary differential type. For comparison and benchmark purposes, a three-dimensional finite element model is developed in Abaqus/CAE to verify the model developed in this study. It is shown that the response of the system is strongly nonsymmetric and that it is essential to retain many degrees of freedom to ensure converged results.

Copyright © 2019 by ASME
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