The scattering of SH wave in a nano elliptical hole embedded the infinite inhomogeneous medium

In this paper, the scattering of SH wave by a nano elliptical hole embedded the infinite inhomogeneous medium is studied. First, the displacement governing equation with variable coefficients is transformed into the complex Helmholtz equation by using complex variable function and conformal transformation. By the wave function expanding method, the analytical expressions of the displacement field and stress field in the inhomogeneous medium are obtained. Considering the surface effect and using the generalized Young–Laplace equation, we obtain the boundary conditions at nano elliptical hole; then the field equations satisfied by the boundary conditions are attributed to solving a set of infinite algebraic equations. The numerical results show that when the size of the elliptical hole reaches the nanometer level, the influences of surface energy, inhomogeneous coefficients, and wave number on the dynamic stress concentration factor near the hole are significant.