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Analytical solution for squeeze film damping of MEMS perforated circular plates using Green’s function

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Abstract

Squeezed air film between two closely spaced vibrating microstructures is the important source of energy dissipation and has profound effects on the dynamics of microelectromechanical systems (MEMS). Perforations in the design are one of the methods to model these damping effects. The literature reveals that the analytical modeling of squeeze film damping of perforated circular microplates is less explored; however, these microplates are also an imperative part of the numerous MEMS devices. Here, we derive an analytical model of transverse and rocking motions of a perforated circular microplate. A modified Reynolds equation that incorporates compressibility and rarefaction effects is utilized in the analysis. Pressure distribution under the vibrating microplate is derived by using Green’s function and also derived by finite element method (FEM) to visualize the pressure distribution under perforated and non-perforated areas of the microplate. The analytical damping results are validated with previous renowned analytical models and also with the FEM results. The outcomes confirm the potential of the present analytical model to accurately predict the squeeze film damping parameters.

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Acknowledgments

This work is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant Number: 2013R1A1A2007684).

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Authors and Affiliations

  1. School of Mechatronics Engineering, Korea University of Technology and Education, 1600 Chungjeol-ro, Byeongchun-myeon, Dongnam-gu, Cheonan, Chungnam, 31253, Republic of Korea

    Asif Ishfaque & Byungki Kim

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  1. Asif Ishfaque
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  2. Byungki Kim
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Correspondence to Byungki Kim.

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Ishfaque, A., Kim, B. Analytical solution for squeeze film damping of MEMS perforated circular plates using Green’s function. Nonlinear Dyn 87, 1603–1616 (2017). https://doi.org/10.1007/s11071-016-3136-z

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  • DOI: https://doi.org/10.1007/s11071-016-3136-z

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