  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, which
we compare to the results of numerical modeling for a few significant cases. At
frequencies above 1 GHz, our model points out the significance of
compressibility effects.
