Nonlinear Vibration and Control of Piezoelectric Laminates

In this paper, the dynamic behavior of piezoelectric laminates is investigated. Thin piezoelectric layers are assumed to be embedded on the top and the bottom surfaces of the rectangular plate. The top and the bottom layers are taken as the actuator and sensor, respectively. Based on Von Karman theory, the geometrically nonlinear relation between strain and displacement is proposed and basic large deformation equations are established. Nonlinear dynamic equations of piezoelectric laminates are formulated using Hamilton’s principle. The Galerkin’s approach is applied to partial differential equations to obtain the ordinary differential equations. The numerical results show the existence of periodic, bifurcation and chaotic motions for the laminated piezoelectric rectangular plate with the changes of frequency and amplitude of forcing loads. Furthermore we can control the vibration of the piezoelectric laminates using a constant gain velocity minus control algorithm. Using the control gain, the free vibration of the plate is damped out more quickly, and the nonlinear dynamic behavior varies from the system without control. Finally, a numerical simulation example shows that the method suggested in this paper is effective and simply.Copyright © 2009 by ASME