Increased accuracy in the application of the Sommerfeld–Watson transformation to acoustic scattering from cylindrical shells

Abstract

The Sommerfeld–Watson transformation (SWT), when applied to problems of sound scattering from elastic bodies with separable geometries, allows the scattered field to be displayed in terms of waves rather than in terms of modes, and so gives a more meaningful picture of the scattering mechanisms at moderate and high frequencies. As typically applied, however, the SWT has left a discontinuity in the calculated field as a function of field point. This discontinuity is not inherent in the method, but is a result of not accounting for the effects of nearby poles in the evaluation of the line integral which represents the geometric part of the scattered field (essentially the specular term). This paper considers this effect in the particular case of broadside scattering from an infinite circular cylindrical elastic shell in an acoustic medium. The scattered field in the backward half-space, as computed from the corrected wave solution, is shown to be in excellent agreement with the field calculated from the normal mode (partial wave) series for frequencies corresponding to ka=1.5 and above, for a steel shell whose wall thickness is one percent of its radius. Shell theory, rather than the theory of elasticity, is used.