Stochastic finite element method for analyzing static and dynamic pull-in of microsystems

Abstract

Electro-mechanical sensors and actuators are a specific type of microsystems. The electrostatic pull-in value is one of the defining characteristics for these devices. Because the material and geometrical properties of micro fabricated systems are often very uncertain, this pull-in value can be subject to considerable variations. Therefore it is important to be able to estimate how uncertainty of mechanical properties propagates to the uncertainty of pull-in values. In this work the required design sensitivities of static and dynamic pull-in are derived. These sensitivities are used to perform a perturbation-based stochastic FEM analysis of an electromechanical device. This stochastic analysis consists of an uncertainty analysis and a reliability analysis. This stochastic analysis is validated by an expensive crude Monte Carlo computation.