Dynamic modeling of geometrically nonlinear electrostatically actuated microbeams (Corotational Finite Element formulation and analysis)

In this paper, a complete nonlinear finite element model for coupled-domain MEMS devices with electrostatic actuation and squeeze film effect is developed. For this purpose, a corotational finite element formulation for the dynamic analysis of planer Euler beams is employed. In this method, the internal nodal forces due to deformation and intrinsic residual stresses, the inertial nodal forces, and the damping effect of squeezed air film are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory using d'Alamber and 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. Numerical examples are presented and compared with experimental findings which indicate properly good agreement.