Dynamic analysis of geometrically nonlinear and electrostatically actuated micro-beams

A complete nonlinear finite element model for coupled-domain MEMS devices with electrostatic actuation and squeeze film effect is developed in this study. For this purpose, a co-rotational finite element formulation for the dynamic analysis of planer Euler-Bernoulli micro-beams 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 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 were compared with those found experimentally, which indicate a very close agreement.