Modeling and Analysis of MEMS in Multi-Physics Fields

An analytical model and a numerical procedure to simulate coupled energy domains in capacitive microdevices are presented. The model consists of a flexible microplate under the effect of electrostatic forces and squeeze film damping. The coupled system is described by the linear plate equation and a modified compressible Reynolds equation to account for the rarefied gas in the narrow gap between the microplate and substrate. A numerical method based on Differential Quadrature Method (DQM) is employed to discretize and solve the coupled differential equations of motion for complex eigenvalues, mode shapes, and quality factors. The simulation results are compared to the experimental data available in the literature. The analysis highlights the effect of air pressure on quality factors and natural frequencies of the coupled system. The developed model provides an effective analysis tool that can be applied to a large class of capacitive devices employing resonant microplates and microbeams.