Squeeze film damping due to flexible and rigid body motion in MEMS: a comparison of analytical, numerical and experimental results

In MEMS [Micro Electro Mechanical Systems] based sensors, squeeze film air damping is the dominant mode of energy dissipation. The analytical solutions are mainly limited to simple geometries with rigid-body-movement based squeeze-motion in MEMS, but very less consideration has been given in literature to estimate damping in MEMS structures that involve both flexible and rigid-body movements based squeeze film action. In this paper, the results from analytical and numerical solutions both for rigid-body case and flexible structures are compared. This comparison is done both at low and high squeeze-numbers. Modal-Projection numerical technique that can account the flexible deformation of MEMS structure is discussed and validated using experimental results of a microstructure operated at high squeeze number or high frequency. It is observed that analytical solutions, based on assumption of uniform-squeeze-motion between rigid-parallel-plates, can significantly over estimate the squeeze film parameters for flexible or elastic structure of a MEMS piezoresistive accelerometer.