Scattering Of SH Waves By Shallow Buried Inclusion In An Radial Inhomogeneous Half Space

With the development of society and the progress of human science technology,elastic wave scattering theory in various fields of the application get more and more widely,such as non-destructive testing,tunnel engineering,earthquake engineering and marine engineering.In order to be more close to the actual engineering application,the research direction is also changed from the homogeneous media to the inhomogeneous medium.The scattering of elastic waves by holes,inclusions,cracks and other scatterers is very mature from numerical to analytical in homogeneous media,But the analytic solution of elastic wave scattering problem in non-homogeneous space has a lot of work to be done.The medium model selected in this paper is a non-homogeneous medium with density change in radial direction,and the model of shallow hole and inclusions is established in half space infinite body.The distribution of dynamic stress concentration factor near the scatterer when the elastic shear wave is incident is studied.Firstly,the research status of continuum mechanics and the research results of wave theory in recent years are briefly introduced.The transformation idea of the variable coefficient Helmholtz equation and the related knowledge of conformal mapping are introduced.Then the Navier-Cauchy equation in the elastic mechanics is obtained according to the equation of motion,the geometric equation and the constitutive relation,and the wave equations of the P-wave and the S-wave are obtained by displacement vector decomposition and separate variable method.Secondly the Helmholtz equation of the variable coefficient is transformed into the standard Helmholtz equation in the mapping medium by complex function method and conformal mapping method,and then the difficult nonuniform problem is transformed into the uniform problem.The expression of incident wave,reflected wave,scattered wave and standing wave in the mapping space and the corresponding stress component form are deduced.The expression of the unknown coefficient in the stress component is obtained according to the boundary condition and the final resultis obtained by Fortran programming.In this paper,the influence of the reference frequency and the inhomogeneity of the incident wave on the distribution of the dynamic stress concentration coefficient in the cavity and the surrounding inclusions in the non-uniform half space are studied.The results will provide the basis for the practical engineering design.