Theory of resonant scattering from spherical cavities in elastic and viscoelastic media

Abstract

Plane incident p-waves which propagate through continuous (possibly absorptive) media are scattered by a fluid-filled spherical cavity contained in it. Using an approach familiar in nuclear scattering theory but novel to acoustics and elastodynamics, it is possible to express the scattering amplitudes (or the partial waves contained in them) for the scattered p-and s-waves in a form which clearly exhibits their dependence on two interacting contributions, one being the broad background of an ideally soft cavity, and the other the superimposed narrow spikes due to resonances excited in the cavity fluid. The cavity appears as a perfectly soft obstacle to the incident waves at all frequencies except in the near vicinity of the cavity eigenfrequencies where there is wave penetration into the filler fluid. When this happens, the interference of this wave with the ’’potential scattering’’ of the background is seen to cause the fluctuating character of the amplitudes (or cross section). We have numerically computed these isolated contributions for a variety of material combinations. The isolated resonances are traced (as Regge pole trajectories) as they reappear at the higher frequencies in subsequent partial waves. Due to its application in the analysis of acoustic-coating performance we have further studied the case of air-filled cavities in lossy rubber. The following findings have emerged: (1) The resonances are comparatively narrow, (2) their locations are apparently independent of the amount of absorption present, (3) absorption only affects the background, (4) shear absorption F1 only affects the mode-converted amplitude fps, and (5) the dilatational absorption, controlled by the parameter F, only influences the nonmode converted amplitude fpp.