Sound scattering and radiation from a thin rod in a viscous medium

Abstract

Sound waves incident on a thin elastic rod whose radius is smaller than the wavelength of the incident sound induce flexural and uniform compressional oscillations in the rod. These elastic oscillations again radiate sound waves into the fluid medium and affect the scattered waves. This synopsis presents theory of sound scattering by, and acousto‐elastic vibrations of, a thin elastic unbound rod in a viscous fluid. The shear viscosity of the fluid was considered in the solutions to the boundary‐value problems concerning the sound scattering and the elastic response of the rod. Results show that the scattered compressional waves consist of the rigid‐rod scattering of compressional wave, a monopolar wave due to the uniform pulsating of the rod, and a dipolar wave due to the flexural vibration of the rod. The scattered viscous waves consist of the rigid‐rod scattering of viscous wave and a dipolar wave due to the flexural vibration of the rod. Acoustic resonances occur when the effective inertia force of the rod balances the stiffness force of the rod. The fluid viscosity and the scattering of sound give rise to radiation damping for the rod vibrations and affect significantly the acoustic resonances.