Hydrodynamic analysis of piezoelectric microcantilevers vibrating in viscous compressible gases

The dynamics of microcantilever beams can be profoundly affected by immersion in fluids. While viscous effects are widely acknowledged to have a strong influence on these dynamics, the influence of fluid compressibility is commonly neglected. Here we experimentally study the hydrodynamic loading effect on a flexural vibrating microcantilever, which is immersed in six different viscous compressible gases. We find that the quality factor prediction from a viscous model shows good agreement with experimental result in the low resonance frequency/mode regime, while the influence of fluid compressibility becomes increasingly important with rising mode number and frequency. In contrast, it is found in all cases that the resonance frequency is independent of the fluid compressibility, which is consistent with the inviscid fluid model's prediction.