Scattering Of Out-plane Waves By Defects Near Interface And Complex Terrain

Scattering of elastic wave by defects near interface and complex terrain is an important subject in elastic wave theory research.Beyond the field of elastodynamics,this paper applies the methods of wave function expansion,complex variable and Green's function to report three kinds of problems:the SH-waves scattering by an elliptical cavity and a crack near bimaterials interface,two scalene triangular hills and a semi-cylindrical canyon,and two triangular hills and a semi-cylindrical canyon with a neighbouring shallow buried cavity.1.6 Green functions were derived for the interface problems:the Green function for the elastic half-space containing an elliptical cavity subject to out-plane harmonic line source loads at arbitrary point along half space surface;the Green function for the elastic half-space containing an elliptical cavity subject to out-plane harmonic line source loads at arbitrary point in half space;the Green function for the elastic half-space containing an elliptical cavityand crack subject to out-plane harmonic line source loads at arbitrary point along half space surface;the Green function for the full elastic half-space subject to out-plane harmonic line source loads at arbitrary point along half space surface;the Green function for the elastic half-space subject to out-plane harmonic line source loads at arbitrary point along half space surface;the Green function for the elastic half-space possessing a crack subject to out-plane harmonic line source loads at arbitrary point along half space surface.2.The SH-waves scattering by an elliptical cavity and a crack near bimaterials interface is reported applying the methods of Green's function and "conformal mapping" in this paper.Based on the idea of "conjunction",the bimaterials is divided along the horizontal interface into an elastic half space possessing an elliptical cavity containing a crack and an elastic half.space while the elliptical cavity coexists with the crack in the uniform media,an elastic half space possessing an elliptical cavity and an elastic half space containing a crack while the elliptical cavity and the crack locate in distincted media.Firstly,the scattering displacement field of half space containing an elliptical cavity is constructed,and the corresponding Green's functions of two half spaces are then deduced.Combined with "crack-division",a crack is created,and thus expressions of displacement and stress are derived while the cavity co-exists with the crack.Undetermined anti-plane forces are loaded on the horizontal surfaces for conjunction of two sections and then solved by a series of Fredholm integral equations based on continuity conditions of the interface.Finally,this paper presents discussion of influence of different parameters such as incident wave numbers,incident angle,the ratio of distance between the center of elliptical cavity and horizontal surfaces and the half long axis length of elliptical cavity,the ratio of distance between the center of elliptical cavity and crackand the half long axis length of elliptical cavity,the length of crack,the angle of crack,and combined parameters of different medium upon the horizontal surface displacement on dynamic stress concentration factors(DSCF)around the elliptical cavity and dynamic stress intensity factors(DSIF)at the crack tip.3.Antiplane response of two triangular hills and a semi-cylindrical canyon,two triangular hills and a semi-cylindrical canyon with a neighbouring shallow buried cavity by SH-waves is studied using wave function expansion and complex function method.Firstly,the analytical model is divided into 3 parts:domain I and III are two triangular hills with semi-cylindrical arc bottom and domain II denotes the other part.The displacement solutions of wave fields are then constructed,which are guarranted to satisfy boundary conditions of the three regions.Three domains are then conjoined to satisfy the "conjunction" condition at shared boundary to derive a series of infinite algebraic equations about the problem combined with the zero-stress condition of semi-cylindrical canyon.Lastly,numerical examples are provided and the influence of different paramiters such as incident angles,wave numbers,the gradient of triangular hills,the radius and depth of the cavity on ground motion is discussed.