Dynamic stress analysis of an elliptical cavity during elastic wave propagation in a density-inhomogeneous medium with the modulus varying as a power function

Abstract

Based on the propagation characteristics of elastic waves in an inhomogeneous continuum, we investigate the dynamic stress concentration caused by an elliptical cavity defect in a complex inhomogeneous continuum with a varying shear modulus and density under the action of SH waves (shear waves with displacement in the horizontal X–Y plane). By introducing the auxiliary function and the shear modulus function to construct the wave field function, the high-order wave equation with a variable coefficient is reduced and simplified and then transformed with coordinate conversion through the conformal mapping method, which allows the standard Helmholtz equation to be solved. Based on this approach, the wave field and stress field are derived by adopting the full-space elliptical cavity scattering model, and the expression of the dynamic stress concentration factor (DSCF) is obtained. Through a numerical example, we analyze the effects of the frequency of the incident wave, the ellipticity of the elliptical cavity, and the inhomogeneity of the medium on the DSCF at the boundary of the elliptical cavity under constant or variable wave velocities. The results show that in the presence of a defect in an inhomogeneous continuum, the dynamic stress concentration that arises when subjected to external forces is profound. Additionally, the value of the DSCF is sensitive to changes in each parameter, and the medium is more likely to be damaged near the position with a larger defect boundary curvature.