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Several studies have been carried out on squeeze film effect especially for micro-electro mechanical systems (MEMS). At the microscale, the gap distance between moving surfaces is very small which can significantly affect the behavior of vibrating MEMS. Thin film layer of fluid can change the frequency response of the MEMS devices by adding stiffness and damping to the structure. The effect of thin film was investigated by coupling the equation of plates with the Reynolds equation. Chaterjee and Pohit [1] presented a semi-analytical reduced order model using the Galerkin method for microcantilever in order to investigate the effect of changing the Kundsen number on the damping coefficient. They made also a comparison with finite element method using ANSYS, showing a good agreement with semi-analytical results. Moreover the method used in ANSYS is modal projection method, which is based on calculating the squeeze stiffness and damping coefficient of the fluid using the eigenvectors of the microplate. However, the determined eigenvalues of the micro-beam do not take into account the change in the resonance frequencies due to the added stiffness.

In this work, we used the Differential Quadrature Method (DQM) on a circular plate to discretize the coupled multiphysics problem. The eigenvalues and eigenvectors are obtained by solving the resulting system. We performed a comparison between the damping coefficients obtained using ANSYS and DQM for the first two bending modes. For low pressure, the two models show a good agreement. However for atmospheric pressure, we have a slight difference between the two models. This is due to the change in the resonance frequency caused by the thin film.

References

[1] Chaterjee S. and Pohit G., Squeeze-film damping characteristics of cantilever microresonators for higher modes of flexural vibration. International Journal of Engineering, Science and Technology 2(4) 187-199 (2010).