Study of natural frequency shifting in a MEMS actuator due to viscous air damping modeled by nonlinear reynolds equation

We report on finite element (FE) modeling and simulation of effect of squeeze-film damping on flexible microstructure operating in ambient air in close proximity to a fixed surface, which is a common case in many MEMS devices. A coupled fluidic-structural problem is solved by applying a nonlinear compressible Reynolds equation, which is derived from the Navier-Stokes equations, transformed into weak form and added to commercial FE modeling software. The proposed model enables investigation of influence of surrounding air on dynamics of different microstructures taking into account air rarefaction and air compressibility effects. The paper presents results of numerical analysis, which aim was to study the phenomenon of natural frequency shifting in the case of free and forced vibrations of the cantilever microstructure. Simulations demonstrate that squeeze-film damping may result in the increase of natural frequency of the microstructure due to system stiffening caused by air compression. The magnitude of this effect is determined by such parameters as ambient air pressure, air-film thickness, vibration frequency and lateral dimensions of the microstructure