Mechanical Behavior of an Electrostatically-Actuated Microbeam under Mechanical Shock

Abstract

In this paper static and dynamic responses of a fixed-fixed microbeam to electrostatic force and mechanical shock for different cases have been studied. The governing equations whose solution holds the answer to all our questions about the mechanical behavior is the nonlinear elasto-electrostatic equations. Due to the nonlinearity and complexity of the derived equations analytical solution are not generally available; therefore, the obtained differential equations have been solved by using of a step by step linearization method (SSLM) and a Galerkin based reduced order model. The pull-in voltage of the structure and the effect of shock forces on the mechanical behavior of undeflected and electrostatically deflected microbeam have been investigated. The proposed models capture the other design parameters such as intrinsic residual stress from fabrication processes and the nonlinear stiffening or stretching stress due to beam deflection.