Numerical investigation into dynamic behavior of electrostatically-actuated circular clamped micro-plate subject to squeeze-film damping effect

The analysis of electrostatically-actuated MEMS devices is complicated since structural deformation alters the nonlinear electrostatic force, which in turn redistributes and modifies the electrostatic coupling effect. The analysis is further complicated by the nonlinear squeeze-film damping effect exerted by the air film between the deformable diaphragm and the fixed substrate. Accordingly, the present study performs a numerical investigation into the effect of this squeeze-film damping phenomenon on the dynamic behavior of a MEMS device incorporating a circular clamped micro-plate. The deflection behavior of the micro-plate is described using an analytical model based on a linearized isothermal compressible Reynolds equation and a sealed pressure boundary condition. In performing the simulations, the model is solved using a hybrid differential transformation and finite difference scheme. The simulations focus specifically on the effects of the residual stress, actuation voltage and excitation frequency on the dynamic response of the membrane.