Nonlinear Analysis of Electrostatic Actuation in MEMS with Arbitrary Geometry

摘要

We present an explicit formulation for the Jacobian (or tangent) matrix of the discretized non-linear model for a coupled electromechanical system. The Jacobian matrix, consisting of the derivatives of the residual, is needed in Newton-Raphson-based algorithms to solve these non-linear problems, as well as in the analysis of their stability. Our formulation of the Jacobian matrix relies on the discretization of the electrostatic sub-model by means of the collocation boundary-element method. It is independent of the discretization method (either boundary or finite elements) and of possible non-linearities in the mechanical sub-model.