Acoustic scattering by elastic spherical shells that have multiple massive internal components attached by compliant mounts

Abstract

A study of the scattering of sound waves by a neutrally buoyant, submerged, spherical shell that has heavy masses internally mounted by springs to the shell is presented. The presence of the attached oscillating masses substantially changes the scattering cross section of the otherwise empty shell. Furthermore, if the compliance (i.e., the spring constants) of the mounts are varied—all else being the same—then the resulting cross section also varies substantially, often by more than an order of magnitude. It is seen that if the incident plane wave impinges upon the shell at its North pole, where the masses are mounted, then the effect of the spring-mass system on the scattering response is strongest. Away from the North pole, this effect weakens; when the incidence is from the South pole, it is weakest. In general, the cross-sectional distortion produced by the attached masses consists of a set of amplitude-modulated resonance features that are computed and displayed in a number of instances. These features seem to be confined around a frequency band containing the main resonances of the (coupled) oscillator formed by the masses. The shell motions are described by the bending theory and also by the exact elasticity theory. Comparing the two, it is possible to determine the limit of validity of the bending theory, which is seen to begin to fail just below the coincidence frequency for this shell. The ‘‘background’’ contribution is separated from the ‘‘resonance’’ contribution associated with the empty shell and also from that associated with the internal oscillator. This triple split, as emerging from a shell theory, does not seem to have been investigated in the past. (Bistatic) angular plots associated with peaks/dips in the backscattering cross section and some of the isolated and symmetric ‘‘rosettes’’ observable in selected cases are displayed. This analytic model is easily reproducible and does not require any special numerical code for evaluation.