Analysis of Bifurcation and Chaos of the Size-dependent Micro–plate Considering Damage

Abstract

In this research, nonlinear dynamics and characteristics of a micro–plate system under electrostatic forces on both sides are studied. A novel model, which takes micro-scale effect and damage effect into account, is established on the basis of the Talreja’s tensor valued internal state damage model and modified couple stress theory. According to Hamilton principle, the dynamic governing equations of the size-dependent micro–plate are derived by variational method and solved via Galerkin method and the fourth order Runge-Kutta method. The effects of damage variable and material length scale parameter on bifurcation and chaos of the micro–plate system are presented with numerical simulations using the bifurcation diagram, Poincare map. Results provide a theoretical basis for the design of dynamic stability of electrically actuated micro- structures.