A Reduced-Order Model for Electrically Actuated Clamped Circular Plates

Abstract

We present an analytical reduced-order model (macromodel) for an electrostatically actuated clamped circular plate. After establishing the equations governing the plate, we discretize the system by using a Galerkin approach. Accordingly, the distributed-parameter equations are reduced to a finite system of ordinary-differential equations in time. We solve the equations for the equilibrium states due to a general electric potential and determine the natural frequencies of the axisymmetric modes for the stable deflected position. Finally, we validate the model by using data from experiments performed on silicon-based microelectromechanical systems (MEMS). The reduced-order model accounts for residual stress, allows for general design variables, and is also robust up to the pull-in instability. Consequently, our macromodel is general and computationally strong enough to be an effective design tool.