Scattering Of SH-wave By Interface Crack And Circular Cavity Near Interface In Bimaterial Vertical Half-space

The scattering of SH-wave are studied in the field of linearly elastic dynamic mechanics in this paper. By using the methods of complex functions and multi-polar coordinates, the Green's function is researched in right-angle plane; the methods of Green's functions and interface conjunction are used to obtain the scattering of SH-wave by circular cavity near bi-material interface in vertical half-space and dynamic stress concentration; and the methods of interface conjunction and crack-division are used to get the influence of scattering of circular cavity near interface with bi-material interface crack impacted by SH-wave.An analytical solution for the Green's function is studied based on the image method, which is the essential solution of displacement field for an elastic right-angle plane with a circular cavity impacted by anti-plane harmonic line source loading at horizontal surface. In this question, owing to the existence of the right-angle plane free surfaces, the elastic wave, which produced by the disturbance of out-plane line source force, is reflected and scattered many times. Thus the solution of displacement field satisfying the stress free boundary conditions is difficult to present. To overcome this difficulty, using image method and muti-polar coordinates method in here, the right-angle plane is extended half space. Then the problem of SH-wave scattering in the right-angle plane can be solved according to the half space with double circular cavity impacted by the out-plane harmonic line source force and the image line source force.The scattering of SH-wave by circular cavity near bi-material interface in vertical half-space and dynamic stress concentration are studied based on the methods of Green's functions and interface conjunction in complex plane. The bi-material media is divided into two parts along the horizontal interface, one of which is elastic right-angle plane with a circular cavity and the other is either elastic complete right-angle plane or elastic right-angle plane with a circular cavity. Then horizontal surfaces of the two half space are loaded with undetermined anti-plane forces in order to satisfy continuity conditions at linking section. So a series of Fredholm integral equations of first kind for determining the unknown forces can be set up through continuity conditions that are expressed in terms of the Green's function. Finally, using the attenuation speciality of SH-wave, the integral equations can be dispersed to linear equations directly, so the numerical solution can be obtained.The scattering of SH-wave by a bi-material interface crack and a circular cavity near interface is also discussed and the solution of dynamic stress concentration factors around circular cavity are obtained. The methods of combination and crack-division are used to make interface cracks. Then horizontal surfaces of the two half space are loaded with undetermined anti-plane forces in order to satisfy continuity conditions at linking section, with some forces to make cracks by means of crack-division technique. For the model of circular cavities near the interface, the added forces at linking interface can be employed to calculate the dynamic stress concentration factors around the edge of circular cavities. Then the problem is summarized into the solution of Fredholm integral equations of first kind by means of the Green's function. Finally, the dynamic stress concentration factors around the circular cavity are discussed to the cases of different parameters in numerical examples.