Transient waves in a thin sphere enclosing an acoustic medium from a moving planar pressure discontinuity

Abstract

Three models are adopted to analyze transient waves in a spherical shell enclosing an acoustic medium from a moving planar pressure discontinuity. The first model is a plane-strain thin ring. The second model is a spherical shell, and the third model is a plane-strain thick ring that modifies the thin ring model to include reflections across the thickness. All models agree that extensional motions of the shell control internal acoustic pressure of the fluid, and that flexural motions modulate average response by a small amplitude high frequency oscillation. The spherical shell model yields a temporary negative pressure opposite to the striking point and a persistent sharp drop in pressure close to the center. Magnitude of transient pressure depends on the separation between the coupled structural resonance and the internal acoustic resonance with pressure release at the boundary.