Scattering Of Transmission SH-wave By A Elliptic Cavity Or Inclusion In A Bi-material Half-pace

The development of elastic wave scattering theory has been for hundreds of years of history,during which the researchers have been listed as key research objects,it uses some methods in mathematical physics has solved some complex problems,the related technology research on Earthquake Engineering,geotechnical engineering and underground structure engineering has important value and practical application.So far,the research on the SH wave scattering theory in the field of researchers can be said that the achievements of excellence,the relevant theoretical models basically have covered the whole space,half space and the 1/4space,has a complete set of theory and data,a huge contribution to the development of wave mechanics.In contrast,elastic wave scattering theory in two-phase medium this branch is only in recent years has been involved in,so research in this area is not comprehensive,which is more lacking in the scattering problem of SH wave transmission defects.In the field of linear elastic dynamics in the study of double phase medium in elastic half space of elliptical hole and elliptical elastic inclusion scattering problems of SH wave transmission,which mainly use the complex function method and Green function method,the method of conformal mapping,polar mobile technology and "fit" thought.The difficulty of this paper is the processing of elliptic boundary and the structure of scattered wave field,which is the key problem to be solved in this paper.In this paper,conformal mapping is used to map the elliptic boundary to the unit circle boundary,which greatly simplifies the problem model,and makes the irregular boundary into the regular boundary.The other two phase medium in elastic half space elliptical holes and elastic Elliptical Inhomogeneity of scattering wave form structure is very difficult,but the research on 1/4 space model is better,this is a reference 1/4 space scattered wave form,the half space of two phase medium along the vertical boundary of "split" into two symmetric distribution of the 1/4 space in the plane in about two on the split surface respectively and uniformly distributed point source load level,the process of SH wave propagation in the vertical boundary satisfy the stress and displacement continuity conditions,and the use of dummy point source method to construct the 1/4 space elliptical holes or elliptical inclusion at the scattering wave displacement field due to a point source loads in the vertical boundary at any position,the Green function which is the structural displacement field,which is related to the The unknown coefficient is solved by the condition of stress and displacement on theboundary of the elliptic hole or the elastic inclusion.The multiple reflection,transmission and scattering will occur in the dual phase medium after SH wave incidence,which makes it difficult to give the corresponding secondary wave form.In this paper,the "mirror image" method is used to transform the half space model to the "mirror image" of the horizontal boundary,so that the original half space model can be transformed into the full spatial model,which can be used to solve this problem.Finally,using the "fit" the idea of the original "open" model "fit" together,establish additional unknown force system of integral equations in the vertical interface,taking into account the SH wave with certain attenuation in the communication process,method for solving the unknown here to use finite truncation of the additional force system.Finally this paper calculated some specific conditions through computer programming,and through the graphical results under different parameters in response to holes and inclusions in transmission of SH wave,the circumferential distribution of the dynamic stress concentration coefficient.It can be the nature of the medium,the transmission of SH wave frequency,incident SH wave incident direction and horizontal boundary angle,elliptical holes and inclusions from the vertical and horizontal boundary boundary distance of elliptic holes and inclusions circumferential dynamic stress concentration distribution had different effects.