ACOUSTIC SCATTERING BY ELASTIC SPHERICAL-SHELLS THAT HAVE MULTIPLE MASSIVE INTERNAL COMPONENTS ATTACHED BY COMPLIANT MOUNTS

A study of the scattering of sound waves by a neutrally buoyant, subme rged, spherical shell that has heavy masses internally mounted by spri ngs to the shell is presented. The presence of the attached oscillatin g masses substantially changes the scattering cross section of the oth erwise empty shell. Furthermore, if the compliance (i.e., the spring c onstants) of the mounts are varied-all else being the same-then the re sulting cross section also varies substantially, often by more than an order of magnitude. It is seen that if the incident plane wave imping es upon the shell at its North pole, where the masses are mounted, the n the effect of the spring-mass system on the scattering response is s trongest. Away from the North pole, this effect weakens; when the inci dence is from the South pole, it is weakest. In general, the cross-sec tional distortion produced by the attached masses consists of a set of amplitude-modulated resonance features that are computed and displaye d in a number of instances. These features seem to be confined around a frequency band containing the main resonances of the (coupled) oscil lator formed by the masses. The shell motions are described by the ben ding theory and also by the exact elasticity theory. Comparing the two , it is possible to determine the limit of validity of the bending the ory, which is seen to begin to fail just below the coincidence frequen cy for this shell. The ''background'' contribution is separated from t he ''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 investiga ted in the past. (Bistatic) angular plots associated with peaks/dips i n the backscattering cross section and some of the isolated and symmet ric ''rosettes'' observable in selected cases are displayed. This anal ytic model is easily reproducible and does not require any special num erical code for evaluation.