<title>Effects of squeezed film damping on dynamic finite element analyses of MEMS</title>

Abstract

The use of micro-fluidics in MEMS device design and implementation is becoming a common practice, especially in the area of biomedical devices. As with all MEMS devices, a validated analysis tool can be invaluable in the design and development process. One of the more common manifestations of micro-fluidics in MEMS design is in the area of squeezed film damping. When one surface moves in close proximity to another solid surface, the fluid in the space between the moving surface and the solid surface can have a significant effect on the dynamics of the moving plate. If the fluid flow in the gap can be assumed to be quasi-steady and viscous-dominant, and if the gap height is small compared to the plate width, the velocity profile of the fluid between the moving plate and the solid surface can be approximated as parabolic in the thickness direction. In this case, the Navier-Stokes equations governing the fluid flow can be reduced to a scalar equation in terms of the fluid pressure. This squeezed film model can be combined with a solid mechanical (finite-element) model in order to perform dynamic fluid-structure interaction analyses for cases in which the above assumptions are valid. In such an analysis, the 3-dimensional solid mechanical model will provide the plate geometry, location, and velocity to the squeezed film model, which will in turn provide the resulting fluid pressure on the moving plate to the solid mechanical model. In this paper, cases will be presented in which the stated assumptions will be validated, and the relevant equations will be derived for both compressible and incompressible fluids. Examples of solid and perforated plates moving in compressible and incompressible fluids will be provided, and their results will be verified against fluid dynamics theory.