Vibration of a Cantilever Beam in Ambient Fluid

TL;DR

This paper derives simple analytical formulas for the vibration response of a cantilever beam in fluid, incorporating viscosity and density, useful for designing viscometers and force sensors.

Contribution

It provides explicit analytical expressions for cantilever vibration in fluid, enabling practical design applications in viscometry and force measurement.

Findings

Explicit formulas include viscosity and density effects.

Applicable to designing viscometers and force gauges.

Simplifies analysis of cantilever vibrations in 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.