Corotational Nonlinear Finite Element Formulation and Modeling of Electrostatically Actuated Microbeams

Abstract

A complete nonlinear finite element model for coupled-domain microelectromechanical system devices with electrostatic actuation and squeeze film effect was developed. for this purpose, a corotational finite element formulation for the dynamic analysis of planer Euler-Bernoulli microbeams considering geometrical nonlinearities due to both large structural deformation and electrostatic actuation is developed. In this method, the internal forces due to deformation and residual stresses, the elemental inertias, and the damping effect of the squeeze-film are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using d'Alembert and the virtual work principles. An incremental-iterative method based on the Newmark direct integration procedure and the Newton-Raphson algorithm is used to solve the nonlinear dynamic equilibrium equations. Several numerical examples are presented and their results are compared with those found experimentally, which indicate a very close agreement.