Comparison of scattering from elastic shells and end-on incident scattering from elastic spheroidal shells

Abstract

Until fairly recently it has not been possible to perform exact calculations of scattering from nonspherical three-dimensional elastic shells. However, due to the extended boundary condition method (EBC) of Waterman, such calculations are presently possible. Both as a check of current numerical codes, and because of an interesting physical observation, a comparison of scattering from submerged spherical shells, and end-on incident scattering from spheroidal shells of the same material are presented in this work. The spherical calculations are performed using a normal mode code and the spheroidal calculations are performed using a code based on the EBC method for aspect ratios ranging from 1 to 3 for two different shell thicknesses. A comparison of the spheroidal form function with that of the spherical case illustrates a one-to-one correspondence between the two in which the form function of the spheroidal cases appear as stretched spherical calculations. This stretching effect is easily explained using the standing wave theory of resonances proposed by Werby and Gaunaurd.