A comprehensive time-domain elasto-acoustics study of a fluid-filled spherical shell embedded in an elastic medium

Abstract

An exhaustive study is carried out on the mechanics of waves travelling through a coupled elasto-acoustic system of a fluid-filled, thick-walled spherical shell embedded in an elastic formation. Important but previously untouched aspects of this classical problem are addressed rigorously. An exact local theory of linear elasticity is applied to the elastic formation and the shell, whereas the linear theory of acoustics for compressible fluids is utilized. Two sets of excitation sources are considered: (i) either incident compressional or shear waves, and (ii) a general traction force acting on either one of the shell's surfaces. The origin of the incident waves can be point sources of stress waves positioned within the infinite elastic medium, shell's material or an eccentric pressure source located within the encapsulated fluid. A unified description of various incident waves in terms of a common set of spherical harmonics having their origin coinciding with the shell's center is proposed. A rigorous cross check of the current approach is performed meticulously against multiple existing limiting cases taken from the pertinent literature. The comparisons lend credence to the current approach and the associated computer code developments. More general situations that emphasize important physical features are considered next. Accordingly, case studies are chosen to represent different geometrical and material configurations when subjected to excitation sources having various origins. The effects of the relative acoustical properties are shown to be very essential in determining the physics of the interaction. Focusing of acoustical energy within an encapsulated fluid or an elastic inclusion, for instance, is determined mainly by the relative celerity of the interacting media. This has practical significance in predicting the likelihood of cavitation in the fluid field as well as the determination of the dynamic stress concentration. Several other important observations are made which have significant practical implications, for instance, in design of shock resistance structures, generation of highly focused ultrasonic pulses for the non-destructive testing or ultrasonic cleaning purposes as well as structural integrity considerations.