theory of in-plane vibrations of nano-mechanical disk resonators in liquids

Characterization of liquids through their shear rheological properties is a well-established approach in different fields of research and industrial applications. micro-electromechanical systems (mems) are among the best solutions for rheology at frequencies up to 100 mhz. nanomechanical resonators enable exploring the rheological properties of liquids at higher frequencies. here, we report on an analytical investigation on the solid-liquid interaction for the in-plane vibration of an elastic disk surrounded by a newtonian liquid. for water, we show that at high frequencies, acoustic radiation is the dominant mechanism in energy loss while at lower frequencies the shear friction dominates. we numerically examine these findings by using the finite element method (fem) in liquid water at frequencies between 200 mhz˷2ghz.