T -matrix approach to study the vibration frequencies of elastic bodies in fluids

Abstract

The T matrix or null field method is used as a computational scheme for analyzing the scattering frequencies of a homogeneous elastic body in a fluid. These frequencies have a unique distribution, in the complex plane, for each body. We solve a scalar transcendental equation to find the scattering frequencies for a sphere. These frequencies are used as starting points in a matrix approach to find the scattering frequencies for a prolate spheriod. Lists and figures of the most important scattering frequencies for a sphere and a prolate spheroid are given.