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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 192891, 7 pages
Research Article

Improving the Validity of Squeeze Film Air-Damping Model of MEMS Devices with Border Effect

Cheng Bai1,2 and Jin Huang1,3

1Research Institute on Mechatronics, Xidian University, Xi’an 710071, China
2Xi’an Communication Institute, Xi’an 710106, China
3Key Laboratory of Electronic Equipment Structure Design, Xidian University, Ministry of Education, Xi’an 710071, China

Received 21 February 2014; Revised 6 May 2014; Accepted 14 May 2014; Published 26 May 2014

Academic Editor: Ricardo Perera

Copyright © 2014 Cheng Bai and Jin Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Evaluation of squeezed film air damping is critical in the design and control of dynamic MEMS devices. The published squeezed film air damping models are generally derived from the analytical solutions of Reynolds equation or its other modified forms under the supposition of trivial pressure boundary conditions on the peripheral borders. These treatments ignoring the border effect can not give faithful result for structure with smaller air venting gap or the double-gimbaled structure in which the inner frame and outer one affect the air venting. In this paper, we use Green’s function to solve the nonlinear Reynolds equation with inhomogeneous boundary conditions. For two typical normal motion cases of parallel plate, the analytical models of squeeze film damping force with border effect are established. The viscous and inertial losses with real values and image values acoustic impedance are all included in the model. These models reduced the time consumption while giving satisfactory result. Without multifield coupling analysis, the estimation of the dynamic behavior of MEMS device is also allowed, and the simulation of the system performance is more convenient.