Studies in Nonlinear Effects of Squeeze Film Damping in MEMS Structures

Structural vibration studies of various MEMS structures have revealed that whenever a suspended flat structure vibrates normal to a fixed substrate with a very small gap between the two surfaces, the squeeze film damping due to fluid present in the gap dominates the dissipation mechanism by orders of magnitude compared with other losses. Since the quality factor is a critical parameter in the design of MEMS devices and it depends on damping, a careful evaluation of the squeeze film damping is necessary. The most often used formulas for evaluating this damping, due to Blech and Griffins, are based on the linearized Reynolds equation. These formulas are applicable for small amplitude oscillations. In this paper, we consider all nonlinear terms in the governing equation of the flow between the plates and study the effects of these terms on the damping characteristics. We show that as the amplitude of vibration increase, the damping force increases faster than the spring force of the fluid and, therefore, the cut-off frequency changes nonlinearly