Iterative Solution of Nonlinear Dynamical System of an Electrostatically Actuated Micro-Cantilever

Abstract

This paper presents an iterative method to solve the nonlinear dynamical system ofan electrostatically actuated micro-cantilever in MEMS. Different from someother iteration methods for nonlinear dynamical systems, no additionalprocedures have to be carried out to eliminate the so-called secular terms. Inaddition, an efficient approach is proposed to expand fractional functions intotruncated Fourier series. That makes it possible to implement the iterativeprocedures. Importantly, all the iteration equations are purely linear. Numericalexamples show that the solutions provided by the method are in excellentagreement with numerical ones. The effects of applied voltage, cubic nonlinearstiffness and squeeze film damping on vibration responses are discussed indetails.