Fluid–structure model for disks vibrating at ultra-high frequency in a compressible viscous fluid

Abstract

Radial mechanical modes of miniature disk-shaped resonators are promising candidates for probing the ultra-high-frequency rheological properties of liquids. However, the lack of an analytical fluid–structure model hinders the inference of liquid properties from the experimental measurement of such radial vibrations. Here, we develop analytical models for the case of a disk vibrating in a compressible viscous liquid. Closed-form expressions for the mechanical quality factor and resonant frequency shift upon immersion are obtained and compared with the results of numerical modeling for a few significant cases. At frequencies above 1 GHz, our model points out the significance of compressibility effects.