Calculation of the transition matrix for the scattering of acoustic waves from a thin elastic spherical shell using the ATILA finite element code

Abstract

The transition matrix, relating the scattered and incident acoustic waves for a thin elastic spherical shell in a free-field environment, has been evaluated using the ATILA finite-element code. A three-dimensional finite-element model of a 0.5-m outer radius, 1-cm thick spherical steel shell surrounded by water was developed. The ATILA code was used to calculate the scattered pressure over the surface of the shell for incident waves represented as products of radial Hankel functions and spherical harmonics. The chosen driving frequency was 474 Hz, corresponding to a value of ka= 1, where k is the wavenumber of sound in water and a is the radius of the shell. The ATILA results were compared with the results of analytical thin shell theory, and were found to agree for a model which divided the spherical shell surface into 72 approximately equal area triangular regions. Also computed for each component was the modal acoustical impedance of the shell. These results agreed within two percent for the zeroth order component and thirteen percent for the first order components.