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Damping and stiffening forces of a squeeze film between two plates

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Abstract

This paper presents the analysis of the squeeze film effect on the MEMS power harvesting devices. The effect of the squeeze film has been represented by the damping effect in previous studies. Our goal, however, is to quantify the stiffening effect, which affects the resonance frequency of the squeeze film and the oscillator system. The finite difference method for rectangular geometries is applied to solve the nonlinear isothermal Reynold’s equation for the squeeze film. The approach is validated by theoretical results for small squeeze numbers. The stiffening effect actually appears as a negative added mass. The damping effect obtained from numerical solutions matches perfectly with the equivalent damping formula derived from the analytical formula. The dynamic response of sinusoidally forced oscillator involving one squeeze film is obtained numerically in order to demonstrate the stiffening effect of the squeeze film. Three main parameters are considered: the initial gap of the squeeze film, the excitation amplitude, and the excitation frequency. The relationship between the amplitude of the steady-state sinusoidal response and the excitation frequency is determined. Numerical results demonstrate that the squeeze film gives rise to both a shift in the resonance frequency at small amplitude oscillations and amplitude dependence of the resonance frequency known as nonlinear hardening. These effects are both observed in experiments.

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  1. Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO, 65211, USA

    Shangyi Chen & Z. C. Feng

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  1. Shangyi Chen
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  2. Z. C. Feng
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Correspondence to Z. C. Feng.

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Chen, S., Feng, Z.C. Damping and stiffening forces of a squeeze film between two plates. Nonlinear Dyn 87, 1763–1772 (2017). https://doi.org/10.1007/s11071-016-3150-1

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