Scattering of a plane acoustic wave from a transversely isotropic cylinder encased in a solid elastic medium

Abstract

A mathematical model is developed to describe the scattering of a plane wave incident at an arbitrary angle on a transversely isotropic cylinder embedded in a solid elastic matrix. The model is based on the normal-mode expansion method, but is complicated by the coupling between the potential functions representing compressional and axially polarized shear waves. The solid matrix around the cylinder precludes the appearance of the leaky Rayleigh modes that dominate the spectrum of a cylinder immersed in a fluid. Instead, interfacial modes contribute to the scattered spectrum—these modes could be instrumental in the development of a nondestructive evaluation technique for the matrix-to-fiber bonds in a fiber-reinforced composite material. The presence of a solid matrix that supports shearing action leads to scattered compressional waves, and shear waves with polarization components in both the axial direction and r-θ planes. The sensitivity of resonances in each of these scattered wave components to perturbations in the cylinder's elastic constants is explored; results indicate that a judicious selection of resonance modes allows characterization of the cylinder's elastic properties.