Finite element modeling of the dynamic response of a MEMS sensor

A finite element formulation is presented for modeling microelectromechanical systems (MEMS) to predict the behavior of dynamic response of piezoelectric ceramics subjected to both mechanical and electrical loadings. The FEM formulation presented is based on variational principle using the concept of virtual work. An unconditionally stable method for direct integration of the equations of piezoelectric material is introduced and can be put in the form of 3-step linear multistep method of second order equations. A thin cantilever plate with PZT sensor mounted on it, is investigated to show the feasibility of analysis using 20 node isoparametric 3D piezoelectric elements, flat-shell elements, transition elements which are implemented for the numerical analysis. Under a given initial loading, a structure would deform accordingly, and the distributed sensor outputs could be calculated at each time step. Such calculation can be used as design tool for MEMS structures containing sensors and actuators.