Sound scattering and radiation suppression by pressurized spherical shells

Abstract

Thin-shell models offer important insights into the complex process of sound-structure interaction but are found to be inconsistent with the rigorous thick-shell theory for fluid-loaded spherical shells. Here, linearized equations of motion of fluid-loaded, thin, spherical shells are re-derived from the first principles. The shell may be prestressed due to the difference in the static pressures in the internal and external fluids. Differences in the fluid-loading terms from previously proposed ad hoc models are identified and their significance is analyzed. Analytic solutions are derived of the problems of spherical sound wave scattering by a fluid-filled, prestressed spherical shell and resonant vibrations of the shell. The results reduce to a number of known exact and asymptotic solutions in appropriate limiting cases. The mathematical model of the shell vibrations is applied to characterize the influence of the shell's material properties and the prestress on passive suppression of low-frequency underwater sound radiation due to diffraction on an acoustically compliant sphere, such as an encapsulated gas bubble. Using soft rubber as the encapsulating membrane is found to preserve the sound suppression qualities of the free gas bubble.