Analytical solutions to single scattering of SH waves by a cylindrical fiber with radially gradient interphases

摘要: In this work, analytical solutions to the single scattering of SH waves by a cylindrical fiber with two specific radially gradient interphase layers are supported based on the method proposed by P.A. Martin (Martin 2002, JASA). In the first case, 1) shear modulus μ(r)=e^2βrand the square of wave number, k^2 , is a linear function of 1/r, and 2) μ(r)=e^(-βr^2 ) and k^2 is a linear function of r^2. For example, analytical solutions to single scattering of SH waves by a Sic fiber with the above two interphase layers embedded in aluminum are presented. The calculated scattering cross sections are compared with values obtained from an approximate method (dividing the continuous varying layer into multiple homogeneous sub-layers). The two methods yield similar results. The contribution of this work benefits the validation of various numerical methods used in the inhomogeneous media.