Scattering of out-plane wave by a circular cavity near the right-angle interface in the exponentially inhomogeneous media

Abstract

By applying the theory of complex function and the image principle, this paper investigate the dynamic stress of wave propagation problems in an exponentially inhomogeneous right-angle plane with a circular cavity. The density is assumed to be an exponential change along x-axis, and the shear modulus is constant. Due to the inhomogeneity, the coefficient of the Helmholtz equation is a variable. Based on the theory of complex function, Helmholtz equation is transformed with a general conformal transformation method. By using the image principle, the right-angle plane is first mirrored as the half-space in order to find the expressions of the incident wave and the reflected wave. Then, the half-space is mapped into the finite one for solving the scattering problem of the wave. In order to verify the validity of this method, wave equation in inhomogeneous media is degenerated to the equation with constant coefficients. By truncating a set of infinite algebraic equations, the coefficient of the series is determined. The expression of scattering wave is given by the traction-free boundary condition. The displacements and stress fields are proposed. Dynamic stress concentration factor (DSCF) around circular cavity is calculated in exponentially inhomogeneous media.