Wave Propagation in Welded Quarter-Spaces

Stress-wave propagation in a composite elastic medium consisting of two homogeneous and isotropic quarter-spaces of different materials, welded together so as to form a half space is considered. The solution by iteration, for the, problem, when one of the quarter-spaces is struck along a line on its plane face, is derived by the method of integral transforms. It is found that in addition to the incident surface and body waves in the medium excited there also exist (i) body waves reflected and refracted from the interface into the two media; (ii) body waves radiated into these media from their common corner (edge line); (iii) Rayleigh waves reflected and transmitted into the media from the corner; and (iv) Stoneley waves or the interface waves (under the usual conditions of their existence) transmitted down the common boundary of the two media. In addition, the occurrence of the ‘allied functions ’ in the solution and their relation to Lamb’s functions are pointed out. 1