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We study steady-state oscillations of an elastic Hele-Shaw cell excited bytraveling pressure waves over its upper surface. The fluid within the cell isbounded by two asymmetric elastic sheets which are connected to a rigid surfacevia distributed springs and modeled by the linearized plate theory. Modalanalysis yields the frequency response of the configuration as a function ofthree parameters: the fluidic Womersley number and two ratios of elastic stressto viscous pressure for each of the sheets. These ratios, analogous to theCapillary number, combine the effects of fluid viscosity and the sheetsinertia, bending and tension. The resonance frequencies of the configurationinclude the resonance frequency of the upper sheet, and the resonance frequencyof both sheets with a constraint of constant gap. Near the resonance frequencyof the upper sheet, the fluid pressure is identical in amplitude and phase tothe external excitation. For configurations where both sheets are nearresonance, small changes in frequency yield significant modification of thefluidic pressure. In addition, a new resonance frequency is observed, relatedto the interaction between motion of fluid parallel to the elastic sheets andrelative elastic displacements of the sheets. The ratio of the amplitude of thefluidic pressure to the external pressure is presented vs. frequency forseveral characteristic solid and fluid properties, yielding a bandpass filterbehaviour. For configurations with a rigid lower surface the pressure ratio isunity at the passband, while for two elastic sheets pressure amplification orreduction occurs near the resonance frequencies. The results presented here mayallow to utilize elastic Hele-Shaw configurations as protective surfaces andmechanical filters.

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