The oscillating and electrostatic characteristics of microelectromechanical system cantilever structure analyzed based on the air gap domain

Abstract

Extensive modeling and simulation of the damping phenomenon, electrostatic actuation, and structural vibration analysis are performed. The governing partial differential equations of cantilever plate are obtained, and the resonant frequencies are calculated from the equilibrium equations. The damping forces of squeeze film are analyzed by obtaining the damping ratio and spring constant. Electrostatic actuation is applied to oscillate the cantilever to ensure that the displacement of the plate is above the thermal noise floor. Electrostatic actuating forces, displacement, and capacitance are calculated both numerically and analytically from the Poisson’s equations. Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Squeeze film effects are simulated by the finite element method. The accuracy of the compact model is studied by comparing its response to the numerical results calculated with the finite element method. The agreement is very good in a wide frequency band. The numerical study and the compact model are directly applicable in predicting the damping force and damping factors of squeeze film.