Creeping-Wave Analysis of Acoustic Scattering by Elastic Cylindrical Shells

Abstract

The Sommerfeld-Watson transformation is applied to the normal-mode solution of a plane sound wave being scattered by an infinite elastic cylindrical shell immersed in a fluid and containing another fluid. The resulting residue series is generated by poles that are the complex zeroes of a 6×6 determinant. These zeroes are found numerically by an extension of the Newton-Raphson method for complex functions. As in our previous work on sound scattering by a solid cylinder, it is found that besides the infinity of the well-known rigid zeroes, there exists a set of additional zeroes that gives rise to generalized Rayleigh and Stoneley waves. The behavior of these zeroes has been studied as function of the wavenumber and also of the shell thickness. The bistatic cross section was evaluated numerically and compared with experiments.