The Dynamic Stress Response Of The Hole Or Inclusion Under Sh Waves In Two-dimensional Inhomogeneous Medium

The study of wave propagation is of great significance,especially the propagation of wave in different types of medium is a major concerned issue all the time,having a wide prospect and future.With the development of science and technology,the problems faced to scholars at home and abroad get more and more challenging.And many experts and scholars are taking research on material science,innovation of the structure,survey of the geology and exploring of the earth's interior.The emphasis of research has been turning from the homogeneous medium into the inhomogeneous medium.Under the background,the research content of this paper is the scattering effect of circular hole and circular inclusion on elastic shear waves(SH waves)under horizontal incidence in a full-space medium where the density changes continuously according a specific law and presents inhomogeneous medium at the edge of the defect.Based on the introduction of the development of the wave problem,this paper discusses the research background and significance of the correspondingly introduces different methods for dealing with inhomogeneous media.At the same time,it gives the requirements of the research methods in this paper.The corresponding basic wave theory and formula derivation.Corresponding functions are used to describe the form of density in an inhomogeneous fullspace medium.The density of the medium changes complicatedly with the change of x and y coordinates.Then the governing equations in the inhomogeneous medium belongs to the Helmholtz equation with variable coefficients in mathematical form and cannot be solved directly.Based on the theory of complex variable functions,using conformal mapping technology to convert the variable coefficient Helmholtz equation into a standard form for solution,the corresponding stress component can be obtained.In order to analyze the scattering effect of circular holes and circular inclusions on SH,the dynamic stress concentration factor(DSCF)at the edge is solved,and the corresponding boundary conditions are introduced to solve the unknown coefficients in the stress,so that the inhomogeneous medium in the whole space can be obtained.In the wave field expression,the DSCF at the corresponding position is further obtained.