Bifurcation and chaotic behavior of micro-plate with size-dependency

This paper investigates bifurcation and chaotic response of a size-dependent micro-plate under electrostatic force applied on its both sides. The size dependency of the micro-plate is taken into account using modified couple stress theory (MCST). Via Hamilton’s principle, the dynamic equations of motion for the micro-plate are obtained. With application of Galerkin procedure and Runge–Kutta (RK) method, the nonlinear partial differential equations are solved numerically. Numerical examples are carried out and the influence of size effect, damping effect and initial gap on chaotic characteristics of the micro-plate system are displayed utilizing Poincare map and bifurcation diagram. The results reveal that complex nonlinear behaviors including chaotic and multiple periodic motions occur in the micro-plate system and the route to chaotic motion is period-doubling. The findings of this research may provide a theoretical guidance for the dynamic stability of electrostatically actuated micro-plate system.