A comparative study of analytical squeeze film damping models in rigid rectangular perforated MEMS structures with experimental results

Abstract

Several analytical models exist for evaluating squeeze film damping in rigid rectangular perforated MEMS structures. These models vary in their treatment of losses through perforations and squeezed film, in their assumptions of compressibility, rarefaction and inertia, and their treatment of various second order corrections. We present a model that improves upon our previously reported work by incorporating more accurate losses through holes proposed by Veijola and treating boundary cells and interior cell differently as proposed by Mohite et al. We benchmark all these models against experimental results obtained for a typical perforated MEMS structure with geometric parameters (e.g., perforation geometry, air gap, plate thickness) that fall well within the acceptable range of parameters for these models (with the sole exception of Blech’s model that does not include perforations but is included for historical reasons). We compare the results and discuss the sources of errors. We show that the proposed model gives the best result by predicting the damping constant within 10% of the experimental value. We study the validity of the proposed model over the entire range of perforation ratios (PR) by comparing its results with numerically computed results from 3D Navier-Stokes equation. These results are also compared with other analytical models. The proposed model shows considerably better results than other models, especially for large values of PR