Scattering Of SH Waves By Inclusion In Density Inhomogeneous Medium

The propagation of SH waves in inhomogeneous medium is a major difficulty in the study of SH waves propagation in complex medium.Inclusions in inhomogeneous medium affect the safety of structures significantly.It is important to study SH waves scattering by inclusions in inhomogeneous medium,and the results can provide reference for the dynamic response of inhomogeneous medium.In this paper,the interactions between the circular cavity and SH waves,the circular inclusion and SH waves in the unbounded density inhomogeneous medium are studied.Firstly,the density function is introduced to describe the unbounded inhomogeneous space.The density of the medium varies with the spatial coordinates in the form of a specific power function.The wave equation in the inhomogeneous medium is a Helmholtz equation with variable coefficients in the mathematical form.Based on complex function theory,the unbounded wave equation is transformed into Helmholtz equation with constant coefficients by conformal mapping method and the stress components corresponding to the wave function in the medium are obtained.According to the stress continuity condition around the circular cavity,the unknown coefficients of various stress components are solved,the scattering wave expression caused by the circular cavity is obtained,and the wave field solution in this space is deduced.Then the scattering of SH waves by circular inclusion in the inhomogeneous medium is studied.According to the continuity conditions of stress and displacement around the circular inclusion,the unknown coefficients are solved.The scattering wave and standing wave expressions are obtained,respectively.Finally,the influence of the density variation parameters,the reference wave number of SH waves,the wave number ratio of SH waves propagating in the medium and the modulus ratio between medium and inclusion on the dynamic stress concentration factor and distribution around the inclusions are analyzed.