Nonlinear Vibration of an Electrostatically Excited Capacitive Microplate

Abstract

This study aims at understanding the transient vibration of an electrostatically excited microplate considering the effects of different boundary conditions. The partial differential equations of motion of rectangular microplate-based microelectromechanical systems (MEMS) are derived within the framework of the classical plate theory and von Kármán geometric nonlinearity. The nonlinear terms are due to the electrostatic force nonlinearity and the mid-plane stretching of the plate. The Galerkin procedure is used to obtain a second-order nonlinear ordinary differential equation in time with quadratic, cubic, quartic, and higher-order nonlinear terms. Attention is focused mainly on the method of elimination of singularity in the electrostatic force; two methods are proposed to treat the singularity. It is indicated that for nondimensional voltages lower than 75, both methods give rise to a similar system response. Finally, an analytical expression representing the transient dynamic behavior of the system is proposed. Experimental verification will be conducted in the next phase of the study.