Sound scattering by cylinders of finite length. II. Elastic cylinders

Abstract

The theoretical results of the preceding article describing scattering from finite length fluid cylinders [T. K. Stanton, J. Acoust. Soc. Am. 83, 55–63 (1988)] are extended to the case of the elastic cylinder. The same method is used: The volume flow per unit length of the scattered field of an infinitely long cylinder is integrated over a finite interval to estimate the scattered field due to a cylinder of finite length. In this article, Faran’s solution for the infinitely long elastic cylinder [J. J. Faran, Jr., J. Acoust. Soc. Am. 23, 405–418 (1951)] is used to derive the scattering from the finite elastic cylinder at angles of incidence normal and nearly normal to the axis. This rigorously derived analytical solution compares very well with backscatter data from Dural cylinders and a scattering model derived by qualitative arguments, both from Andreeva and Samovol’kin [I. B. Andreeva and V. G. Samovol’kin, Akust. Zh. 22, 637–643 (1976) and Sov. Phys. Acoust. 22 (5), 361–364 (1976)]. The conclusions of this work and from Andreeva and Samovol’kin are the same: The acoustic or effective length of a cylinder, whether it be infinitely long or of finite length, is the smaller of L or the radius of the first Fresnel zone (rλ)1/2, where L is the length of the cylinder or of the insonified ‘‘spot’’ of a longer cylinder, r is the distance from the cylinder to the field point or receiver, and λ is the acoustic wavelength.