Vibratory MEMS and Squeeze Film Effects

Abstract

Vibratory MEMS devices typically consist of a plate like structure that oscillates out of plane and thus generally normal to a fixed substrate. These structures have a trapped air-film between the structure and the fixed substrate either by design or by partial vacuum packing. The trapped air behaves like a squeeze film offering both stiffness and damping to the structure. A good estimate of squeeze film forces is important for predicting the dynamic performance of such devices. In this chapter, we discuss the development of squeeze film modeling, going back to its origins in the lubrication theory. We explain the derivation of Reynolds’ equation that governs the squeeze film flow and review some of the major analytical modeling techniques. A detailed analytical solution using the Eigen expansion technique that incorporates the effect of structural elasticity using approximate mode shapes is presented. We also discuss finite element based simulations for finding the squeeze film forces. We present a simple example analysed using an implementation of the finite element formulation discussed. We also summarize the experimental studies reported in the literature that have shaped both analytical and numerical models.