Scattering Of SH-Wave By An Interface Cavity Of ARbitrary Shape And The Crack At Its Edge

The scattering problems of SH-waves are studied in this paper by an interface arbitrary-shape-cavity as well as collinear cracks or interface cracks originating diametrically at the cavity edge in the field of linearly elastic dynamic mechanics. The methods of complex function and Green's function are used here. At first we should construct a suitable Green's function, which is an essential solution to displacement field for an elastic half space with an arbitrary-shape-canyon impacted by antiplane harmonic line source loading at horizontal surface. Then we consider the problem as a "conjunction" problem: According to the solutions for wave problem in interface between two conjunctive homogeneous elastic half-spaces as well as the scattering problem of SH-waves by an arbitrary-shape-cavity in homogeneous material, we divide the elastic space with an interface cavity into two parts along the interface, each is elastic half space with an arbitrary-shape-canyon. And then dividing surfaces are loaded with undetermined antiplane forces, and with some antiplane reacting forces to appear cracks. Finally, 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 the integral equations can be transformed into a series of algebraic equations based on the direct-discrete method and solved numerically. The works in detail are as follows:1 .Base on the essential solution for a complete elastic half space impacted by antiplane line source loading at horizontal surface, the essential solution of displacement field for an elastic half space with an arbitrary-shape-canyon impacted by antiplane harmonic line source loading at horizontal surface is constructed by using the method of complex function and conformal mapping. That is the special Green's function suitable for this paper. The method of conducting and deducing Green's function is provided, so does the discussing about properties of this Green's Function.2.The problem about dynamic stress concentration around the interface arbitrary-shape-cavity incidenced by SH-waves is investigated. By means of "conjunction", the model of this problem is established. And then a series of Fredholm integral equations of first kind can be set up in terms of the Green's function, furthermore the scattering problem of SH-wave by cavity in the interface is transformed into a series of algebraic equations based on the direct-discrete method. The expressions of DSCF around the interface arbitrary-shape-cavity arededuced. Numerical results of DSCF are provided when the cavity is ellipse, square and diamond. The influences of wave numbers, angle of incidence, combination of different media parameters and cavity shape upon the DSCF around the cavity are discussed.3.The solutions to scattering of SH-wave by an interface arbitrary-shape-cavity for far-fields are studied. Base on the solutions for near-fields, the special properties for far-fields are investigated. And then the solutions for displacement mode of scattering wave at far field and scattering cross-section are provided at the interface cavity when it is ellipse and diamond. The influences of cavity shape, property of media, wave numbers and angle of incidence upon the property of scattering wave at far-fields are discussed.4. Scattering of SH-wave by a radial collinear crack at the edge of arbitrary-shape-cavity in isotropy media is studied. The solution of DSIF at crack tips is obtained. The method of crack-division is used to make radial cracks at the edge of cavity. A series of integral equations for determining the DSIF at tips of anti-plane crack are set up in terms of the Green's function. Numeral results of DSIF at radial crack tips of ellipse and square cavities are provided. Then the influences of different shape cavities upon the DSIF at the crack of their edges are discussed.5.Scattering of SH-wave by a radial interface crack at the edge of arbitrary-shape-cavity is studie...