Scattering of cylindrical inclusions in half space with inhomogeneous shear modulus due to SH wave

Abstract

Dynamic responses around cylindrical inclusion in inhomogeneous medium are discussed. A mathematical model of inhomogeneous half space is established. The shear modulus of the medium is assumed to change in two dimensions. Based on complex function theory, the governing equations are derived. Meanwhile, the auxiliary function is introduced. By solving the governing equation, the analytical expressions of the displacement field and stress field formed by Bessel function and Hankel function are obtained. The unknown coefficients can be obtained by boundary conditions. According to numerical examples, the results of this paper are compared with published results to verify the validity of the method. Meanwhile, the effects of inhomogeneous parameters, reference wave number and burial location on the dynamic stress concentration factor (DSCF) around a cylindrical inclusion are discussed.