Nonlinear Dynamics of Multilayered Microplates

Abstract

This paper, for the first time, investigates the nonlinear forced dynamics of a three-layered microplate taking into account all the in-plane and out-of-plane motions. The Kirchhoff's plate theory, along with von Kármán nonlinear strains, is employed to derive the nonlinear size-dependent transverse and in-plane equations of motion in the modified couple stress theory (MCST) framework, based on Hamilton's energy principle. A nonconservative damping force of viscous type as well as an external excitation load consisting of a harmonic term is considered in the model. All the transverse and in-plane displacements and inertia are accounted for in both the theoretical modeling and numerical simulations; this leads to further complexities in the nonlinear model and simulations. These complexities arising in the theoretical model are overcome through the use of a well-optimized numerical scheme. The effects of different layer arrangements and different layer material percentages on the force–amplitude and frequency–amplitude curves of the microsystem are investigated. The results of this study shed light in the nonlinear resonant behavior of multilayered microplates and could be helpful in design and analysis of multilayered microplates in microelectromechanical systems (MEMS) applications.