Frequency Response and Resonance of Elastic Hele-Shaw Cells with Application to Mechanical Filters

Arie Tulchinsky; Amir D. Gat

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arXiv · 1704.03175

Frequency Response and Resonance of Elastic Hele-Shaw Cells with Application to Mechanical Filters

Arie Tulchinsky·Amir D. Gat

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Abstract

We study steady-state oscillations of an elastic Hele-Shaw cell excited by traveling pressure waves over its upper surface. The fluid within the cell is bounded by two asymmetric elastic sheets which are connected to a rigid surface via distributed springs and modeled by the linearized plate theory. Modal analysis yields the frequency response of the configuration as a function of three parameters: the fluidic Womersley number and two ratios of elastic stress to viscous pressure for each of the sheets. These ratios, analogous to the Capillary number, combine the effects of fluid viscosity and the sheets inertia, bending and tension. The resonance frequencies of the configuration include the resonance frequency of the upper sheet, and the resonance frequency of both sheets with a constraint of constant gap. Near the resonance frequency of the upper sheet, the fluid pressure is identical in amplitude and phase to the external excitation. For configurations where both sheets are near resonance, small changes in frequency yield significant modification of the fluidic pressure. In addition, a new resonance frequency is observed, related to the interaction between motion of fluid parallel to the elastic sheets and relative elastic displacements of the sheets. The ratio of the amplitude of the fluidic pressure to the external pressure is presented vs. frequency for several characteristic solid and fluid properties, yielding a bandpass filter behaviour. For configurations with a rigid lower surface the pressure ratio is unity at the passband, while for two elastic sheets pressure amplification or reduction occurs near the resonance frequencies. The results presented here may allow to utilize elastic Hele-Shaw configurations as protective surfaces and mechanical filters.

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Arie Tulchinsky, Amir D. Gat. 2017-04-11. Frequency Response and Resonance of Elastic Hele-Shaw Cells with Application to Mechanical Filters. https://arxiv.org/abs/1704.03175

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