Nonlinear modeling of squeeze-film phenomena

Oscillating microplates attached to microbeams is the main part of many microresonators and micro-electro-mechanical systems (MEMS). The sque-eze- film phenomena appears when the microplate is vibrating in a viscose medium. The phenomena can potentially change the design point and performance of the micro-system, although its effects on MEMS dynamic are considered secondary compared to main mechanical and electrical forces. In this investigation, we model the squeeze-film phenomena and present two nonlinear mathematical functions to define and model the restoring and damping behaviors of squeeze-film phenomena. Accepting an analytical approach, we present the mathematical modeling of microresonator dynamic and develop effective equations to be utilized to study the electrically actuated microresonators. Then employing the averaging perturbation method, we determine the frequency response of the microbeam and examine the effects of parameters on the resonator's dynamics. The nonlinear model for MEMS includes the initial deflection due to polarization voltage, mid-plane stretching, and axial loads, as well as the nonlinear displacement coupling of the actuating electric force. The main purpose of this chapter is to present an applied model to simulate the squeeze-film phenomena, and introduce their design parameters.