Dynamic stress responses of defects in periodic heterogeneous media under SH waves

Abstract

Due to the complexity of heterogeneous medium models, the corresponding research methods still have great limitations, and hence, there is a dearth of research findings. To study the problem of dynamic stress concentration in heterogeneous media, the scattering of SH waves by circular holes in a full-space periodic heterogeneous continuum medium is investigated based on the propagation characteristics of elastic waves in complex heterogeneous media. The wave equation of SH waves propagating in heterogeneous media with the elastic shear modulus and density varying in the form of trigonometric functions is solved by using the complex function method, the wave function expansion method, and the auxiliary function method. On this basis, the wave field and stress field are derived, and the expression of the dynamic stress concentration factor (DSCF) on the boundary of a circular hole is given. The effects of the reference wavenumber and the variation period of the heterogeneous medium on the distribution of the DSCF on the boundary of a circular hole are analyzed through numerical examples. The results show that when the circular hole defect is within one heterogeneous period of the medium, shortening of the heterogeneous period of the medium reduces the peak of the DSCF due to high-frequency waves on the boundary of the circular hole.