Vibrations of a thin, prestressed, fluid-loaded spherical shell forced by a point sound source

Abstract

This paper investigates vibrations of and sound scattering by a thin elastic spherical shell when static pressures are different in the fluids inside and outside the shell. The work is motivated by stratospheric balloons being employed to carry acoustic sensors and by the proposed use of large, encapsulated gas bubbles for passive suppression of underwater sound [O. A. Godin and A. B. Baynes, J. Acoust. Soc. Am., 143, EL67–EL73 (2018)]. Linearized equations of motion of thin, prestressed shells are derived from first principles. Differences in the fluid-loading terms from previously proposed ad hoc models are identified and their significance is analyzed. Analytic solutions are derived for vibrations of a spherical shell excited by an incident spherical sound wave and for acoustic fields in the internal and external fluids. The results are verified against exact solutions in several particular cases. The mathematical model of the shell vibrations is applied to characterize the influence of the shell’s material properties on passive suppression of underwater noise and to quantify the effect of wave scattering by the balloon on performance of balloon-borne infrasound sensors in the atmosphere. [Work supported by ONR.]