The acoustic scattering by a submerged, spherical shell. III: Pole trajectories in the complex-k a plane

Abstract

Previously, a fundamentally oriented analysis was presented of the complex-ka plane pole structure of the S matrix for a thin spherical shell for 0<ka<100 [Sammelmann et al., J. Acoust. Soc. Am. 85, 114–124 (1989)]. In this analysis, it was concluded that fluid loading the first antisymmetric mode of the shell in vacuum had a rather violent effect; the mode bifurcated into two distinct modes near the coincidence frequency. In this article, the relationship of the poles of the diffractive modes of impenetrable spheres and the eigenfrequencies of the shell in vacuum to the modes of the fluid-loaded shell are precisely established by studying the complex-ka plane trajectories of the S-matrix poles under variations of the material parameters of the shell. The evolution of these modes are also examined as the shell thickness is varied from 2% to 50% of the outer radius of the shell. It is found that the limit of an elastic solid is not approached smoothly and that modal reorganizations similar to the bifurcation phenomenon noted above is a common occurrence. The implications of this behavior are examined for both the complex-ka, real-l and the real-ka, complex-l pictures.