Dynamic Stress Analysis of SH Waves Scattering Around a Circular Cavity in Inhomogeneous Medium

Abstract

Introducing a density function to characterize the inhomogeneous unbounded space. Based on the principle of homogenization, use the complex variable function method to investigate harmonic dynamics stress of the radially inhomogeneous medium with a circular cavity. In polar coordinates, where the density of the medium changes, the density is only positively correlated with the radial direction and the shear modulus in the medium is constant. Due to the continuous change of the density, the standard Helmholtz equation when SH waves propagate in the unbounded space of constant density will become a Helmholtz equation with variable coefficients. This equation can be equivalently transformed into a standard Helmholtz equation by Conformal Transformation Method (CTM). And then, the displacement field and stress field in the inhomogeneous medium can be proposed, they can be inferred from the equilibrium differential equation that the wave fields must satisfy. The changes in density parameter of the medium further affect the dynamic stress concentration factor (DSCF) around the circular cavity.