Nonlinear Dynamic Response and Vibration Active Control of Piezoelectric Elasto-plastic Laminated Plates with Damage

Abstract

Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion that is related to the spherical stress tensor is proposed to describe the mixed hardening of damaged orthotropic materials, the dimensionless form of which is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations of orthotropic materials are established. The electric potential distribution along the thickness direction of the piezoelectric sensor layer is determined by adopting the quadratic Lagrange interpolation, and the incremental electric charge equilibrium equation is built according to the Maxwell equation. In addition, by using the classical nonlinear plate theory, the incremental nonlinear dynamic governing equations of the piezoelectric elasto-plastic laminated plates with damage are obtained. Meanwhile, an analytical model for the vibration control of the system is proposed by introducing the negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects. The finite difference method and the Newmark- β method are adopted to make the undetermined variables discretized in the space and time domains, respectively, and the whole problem is solved by the iterative method. In the numerical examples, the effects of damage, piezoelectricity, feedback control gain and the piezoelectric position on the nonlinear vibration of piezoelectric elasto-plastic laminated plates are discussed in detail, and the differences between the piezoelectric elastic laminated plates and piezoelectric elasto-plastic laminated plates are analyzed.