Improvements to the Mathematical Model of Acoustic Wave Scattering from Transversely Isotropic Cylinders

Abstract

This paper considers the scattering of an in nite plane acoustic wave from a long immersed, solid, transversely isotropic cylinder. The mathematical model which has already been developed for this problem does not work in the case of a normally incident wave. Modi cations to the mathematical model are proposed in order to make it applicable to all incidence angles, including = 0. Numerical results are used to demonstrate the correctness of the modi ed equations. Moreover, using a mathematical discussion, it is shown that at normal incidence, the whole displacement eld is constrained within the isotropic plane of the cylinder (cylinder cross section) and only the two elastic constants characterizing this plane appear in the remaining equations. A perturbation study on the ve elastic constants of the transversely isotropic cylinder con rms this result.