Creeping-Wave Analysis of Acoustic Scattering by Elastic, Cylindrical Shells

Abstract

The Sommerfeld-Watson transformation is applied on the normal-mode solution of a plane 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 six-by-six determinant. These zeroes are found numerically by an extension of the Newton-Raphson method for complex functions. It is found that besides the infinity of the well-known Franz's zeroes there exists a finite number of additional zeroes, which generate generalized Rayleigh and Stonely waves. These latter zeroes owe their existence solely to the elastic properties of the scatterer; they disappear in the limits of zero or infinite rigidity. Scattering cross sections are presented for various elastic and geometric parameters of the shell.