Vibration of a Cantilever Beam in Ambient Fluid

Abstract

Here we obtain analytical expressions for the frequency response of a cantilever beam in the presence of ambient fluid. The advantage of our approach, besides its simplicity of use, is that it explicitly contains the viscosity and the density of the ambient fluid. Thus, if measuring the frequency spectrum, the expression can be used in the design of viscometers. Conversely, if the ambient fluid is known, the expression can be used in the design of force gauges such as in Atomic Force Microscopy.