Frequency Response of a Viscously Damped Flat Plate

Abstract

The frequency response of a flat plate in a viscous fluid is a problem with applications in microsystems, including gyroscopes, accelerometers, viscometers, and biological sensing. To find the frequency response away from the resonant frequency, the equations of motion are combined with the solution to Stokes’ second problem to produce an analytic solution for the motion of the plate in response to a sinusoidal driving force. These results are used to determine the gain, phase lag, and dynamic stability of the system. The behavior of the system depends on an effective damping ratio ζeff, which depends on the resonator dimensions, and is proportional to the square root of the viscosity times the fluid density.