Effect of air damping on the dynamics of nonuniform deformations of microstructures

In this paper, we present a methodology for extracting macromodel parameters of compressible isothermal squeezed-film damping (CISQFD) for flexible structures of MEMS under small amplitude oscillation. The theoretical derivation, which is based on structural modal analysis and CISQFD numerical simulation, is presented. The spring and damping components of CISQFD of any oscillation mode can be extracted by this methodology, and thus the generic parameters of CISQFD can be obtained for any flexible structure with given oscillation modes. We successfully formulated an accurate and concise second order dynamics equation for a flexible MEMS devices by using the CISQFD parameters and the modal spring constant and mass. Simulation results of resonance shift and quality factor are consistent with experimental results