Mechanical analysis of circular hole affected by rigidity in inhomogeneous medium under anti-plane shear wave

Based on the theory of complex variable function, the propagation properties of anti-plane shear wave in inhomogeneous right-angle space are analysed. The inhomogeneity of the medium is reflected in the fact that the shear modulus is a function related to spatial coordinates. A displacement auxiliary function and a pair of mapping functions are introduced to assist in deriving the governing equation. Meanwhile, the transformation between coordinates can be more convenient in the complex coordinate system. The wave field expressions of reflected and scattering waves are constructed by using the image method. The unknown coefficients in the scattering waves are solved according to the boundary condition of the circular hole, and the analytical expressions of the wave field in the right-angle space are given. In dynamic analysis, rigidity can be expressed by shear modulus. In the analysis of numerical examples, the dependence of displacement amplitude and dynamic stress concentration factor (DSCF) on the inhomogeneous parameter, reference wave number, and the position of circular hole are discussed.