A variational beam model for MEMS driven by electrostatic and piezoelectric forces

Abstract

A size-dependent model of a micro-electromechanical system (MEMS) actuated by both electrostatic and piezoelectric forces is proposed based on the modified couple stress theory. The governing equation and boundary conditions are derived with the help of the Hamilton principle and solved numerically by employing the Galerkin method and Newton downhill method. A material length scale parameter (MLSP) is incorporated in the model to capture the size effect in microstructures. The results show that the piezoelectric voltage on the beam can reduce the electrostatic voltage dramatically and may guide the design of micro-devices.