A reduced-order model for electrically actuated clamped circular plates

We present an analytical reduced-order model (macromodel) for an electrically actuated clamped circular plate. After establishing the equations governing the plate, we discretize the system by using a Galerkin approach. The distributed-parameter equations are then reduced to a finite system of ordinary-differential equations in time. We solve these 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 attempt to validate the model by using data from experiments performed on silicon-based microelectromechanical systems (MEMS). The reduced-order model accounts for both geometric nonlinear hardening and 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.