Generalized Debye Series Theory for Acoustic Scattering: Some Applications

The problem of propagation of acoustic waves in the presence of a submerged elastic object of cylindrical or spherical shape is formulated here in a unified fashion. With this general formalism is associated a synthetic procedure of resolution of the continuity conditions for the fields at the interfaces. This procedure, based on the operator concept, leads in a simple and direct fashion to the generalized Debye series for the exact solution of wave propagation in the case of separable geometries with the acoustic source either inside or ouside to the scatterer. For cylindrical and spherical geometries, this result, which we term the "Generalized Debye Series Theory" (GDST), is exploited for various applications and appears as a complementary contribution to the Resonance Scattering Theory (RST) as established by H. Überall et al.