Vibration Response of Elastic Disks in Surrounding Fluid: Viscous Versus Acoustic Effects

Abstract

The vibrations of thin, elastic, circular disks such as musical cymbals, hard disk drives, and microscale resonators are significantly influenced by the presence of a surrounding fluid. The energy of disk vibrations is known to dissipate into viscous losses and to radiate away as sound. However, the relative importance of these mechanisms is not well understood. In this paper, we present three-dimensional computations of the fluidic impedance of thin, elastic disks vibrating with small amplitudes under ambient conditions. These computations encompass both macroscale and microscale disks, a wide range of operating frequencies, and different fluidic environments. Viscous fluidic impedances are computed using a finite element model, whereas acoustic fluidic impedances are computed using a boundary element method. For a disk with a given clamping ratio vibrating in a specific mode, the nondimensional viscous impedance depends on the unsteady Reynolds number, while the nondimensional acoustic impedance depends on the ratio of structural to acoustic wavelengths. It is shown that viscous losses dominate the fluid damping of disks in data storage and circular saw applications and of conventional disk microresonators. However, for ultrahigh frequency resonators, acoustic radiation must be taken into account to correctly estimate the overall fluid damping. The computed fluidic impedances are expected to be an important aid in the design of a wide range of disk resonators up to the megahertz regime.