Explicit Solutions to Single Scattering of SH Waves with a Radially Gradient Interphase Layer

Abstract

In this work, analytical solutions to the single scattering of horizontally polarized shear waves (SH) by cylindrical fibers with two specific radially gradient interphase layers are presented. In the first case, the shear modulus μr=e2βr and the square of wave number k2 is a linear function of 1/r; in the second case   μr=e−βr2 and k2 is a linear function of r2. As an example, we solve the single scattering of SH waves by a SiC fiber with the two interphase layers in an aluminum matrix. The calculated scattering cross sections are compared to values obtained by an approximate method (dividing the continuous varying layer into multiple homogeneous sublayers). The results indicate the current approach gives excellent performance.