T-Matrix Analysis of Acoustic Wave Scattering from Thin Elastic Shells.

Abstract : Progress has been made in the study of acoustic wave scattering by elastic obstacles immersed in water using the T-matrix approach. It is understood, that in problems of interest to the Navy, scattered field data is required for long, thin bodies of revolution whose wall thickness is very small compared to the wavelength of the incident wave but whose overall dimensions are comparable and often larger than the wavelength of the incident wave. This project was begun to precisely address such problems, taking into account and exploiting the thinness of the shell. We propose to use shell theory equations rather than the full elasticity equations in region I in order to avoid some of the complications. Shell theory reduces the partial differential equations in three coordinates to a higher order equation in two coordinates. All description of the displacement and stress fields is made with respect to a reference surface in the shell. Now, it is no longer necessary to invoke integral representations to describe the elastic field in this region. One extracts from the shell equations an expression for the impedance matrix of the shell which is then interfaced with the T-matrix approach for acoustic wave scattering problems.