Frequency response of cantilever beams immersed in compressible fluids with applications to the atomic force microscope

The dynamics of microcantilever beams can be strongly affected by immersion in fluid. While the importance of viscosity for devices of microscale dimensions is well established, the significance of fluid compressibility has not been investigated in detail. Here, we present a rigorous theoretical model for the frequency response of a rectangular cantilever beam that is executing normal and torsional oscillations, and is immersed in a compressible fluid. Both the viscous case and the inviscid limit are considered, and the model is valid for arbitrary mode number. We find that compressibility becomes increasingly important as the mode number rises. This is particularly relevant for gases, where compressibility is found to be important for high mode numbers of practical interest.