The Scattering Of SH Wave In The Semi Circular Hollow In A Non Uniform Half Space

With the development of science and technonogy,scholorers have change their research focus from the homogeneous material to inhomogeneous material about geology?structure?materials and the inner structure of the earth. A large number of scholars have carried out the related research on the circular hole, inclusion and crack in the case of homogeneous medium.In this case,two kinds of inhomogeneous media with density changing belong to some Specific rules have been selected to research the dynamic stress concentration and the corresponding surface displacement when a SH wave scattered a semi-cylindrical canyon .In this paper, we firstly introduce the theory of wave theory and discuss the background of the theory of elasticity. At the same time, we introduce the development of the theory about inhomogeneous medium wave in the global. And then we describe the ideas which we inspired about changing the variable coefficient inhomogeneous wave equations to homogeneous. The following are the influence about the stress concentration and the knowledge of conformal mapping. Then we process the basic equation and get the displacement motion equation of elastodynamics. Keep the processing,we can get the equation which represent the horizontal and longitudinal waves respectively undering the time harmonic condition. Using the conformal mapping ,we can get the standard Helmholtz equation by changing the inhomogeneous into homogeneous.The expression of the incident wave, reflected wave and scattered wave is obtained by establishing the model of the elastic half space interface with a semi-cylindrical canyon.Finally, the unknown coefficients and the expression of dynamic stress concentration factors(DSCF)are obtained by using the corresponding boundary conditions. The corresponding results are calculated by Fortran program.