Nonsymmetric Nonlinear Dynamics of Piezoelectrically Actuated Beams

Abstract

The nonlinear behavior 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 the piezoelectric patch and the beam. Through use of the generalized 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 utilized 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 using 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.