Frequency Response of Cantilever Beams Immersed in Viscous Fluids

The dynamic response of microcantilever beams is used in a broad range of applications, including ultra-sensitive mass measurements and imaging with molecular and atomic scale resolution. This chapter presents an overview of the theoretical models for the fluid-structure interaction of cantilever beams immersed in viscous fluid. The focus is on beams whose lengths greatly exceed their widths, as is often encountered in practice. The chapter also presents the two-dimensional theory for flexural modes at low mode number, where fluid viscosity plays an essential role. Models for torsional, in-plane and extensional modes, also at low mode numbers, are summarized in the chapter, respectively. The chapter describes the general, three-dimensional theory for arbitrary mode order, with a focus on the flexural modes. Both incompressible and compressible flows are discussed, accompanied by scaling analyses for determining the regimes where fluid compressibility is expected to be important.