Application Of Wave Function Expansion In Scattering Of Elastic Waves

Diffraction of Elastic Waves and Dynamics Stress Concentrations has great academic significance and distinct referenced value in practical project..Based on this as engineering background, an analytical solution of incident SH waves by some kind of representative site in a half-space is presented.A closed-form solution for two-dimensional scattering of plane SH waves by a tunnel of circular-arc cross-section in a half-space are presented by using the region division and auxiliary functions methods as well as the wave functions expansion.Based on convergence and error analyse, the effects of the frequency of the incident waves,the shape and position of tunnel on displacement amplitude of ground surface and hoop stress amplitude on the wall of tunnel are illustrated.The results indicate:The incidence angles and the frequency of the incident waves,as well as the shape and position of tunnel,all have influence on displacement amplitude of ground surface.By expressing all displacement and stress waves as cosine functions,a closed-form solution for two-dimensional scattering of plane SH waves by a semi-cylindrical heterogeneous hill are presented using the wave functions expansion.For the solution to be correct,the computed stress and displacement residual amplitudes were showen to be numerically negligible everywhere,including those at both rims of the hill.Displacements at higher frequencies are also computed. The results indicate the effects of rigidity of the hilly region on the surface ground displacements of the hill and its adjacent region are siginificantly strong.Using the improved accurate closed-form wave function analytic solution,the solution of two-dimensional scattering and diffraction of plane SH waves by a semi-cylindrical hill with a semi-cylindrical or cylindrical concentric tunnel inside an elastic half-space was reformulated.Similarly, stress and displacement residual amplitudes were showen to be numerically negligible everywhere. Displacements at higher frequencies are also computed,as well as great radius of tunnel.In the end, the effects of the frequency of the incident waves,the shape and radius of tunnel on displacement amplitude of ground surface are illustrated.