Acoustic wave scattering from transversely isotropic cylinders

Abstract

Mathematical expressions are derived for the far-field backscattering amplitude spectrum resulting from oblique insonification of an infinite, transversely isotropic elastic cylinder by a plane acoustic wave. The normal-mode solution is based on decoupling of the scalar potential representing the horizontally polarized shear wave from those of the compressional and vertically polarized waves. The solution degenerates to the well-known simple model for isotropic cylinders in the case of very weak anisotropy. The solution is used to study the influence of each element of the stiffness matrix on the various resonant modes of vibration. Perturbations of the elements c33 and c44, which characterize the cylinder along the axis, significantly affect resonant frequencies corresponding to axially guided waves. Perturbations of c11 and c12, which characterize the material on the transverse plane, predominantly affect the Rayleigh and Whispering Gallery resonance frequencies. Perturbations of c13 affect all three types of resonances. These results are consistent with elasticity theory and the known modal shapes of these resonances.