Scattering Of Plane SH Waves By An Arbitrary Shape Hill

Site response problems are a kind of important problems in earthquake engineering. A lot of investigations of earthquake damage show that the existence of local sites affects the scattering and diffraction of seismic wave greatly. Accordingly, there are sensitive change of earthquake response of ground surface, underground structure and buildings in narrow spatial dimension. The local sites influence distribution of earthquake damage therefore. Hence, the investigation of analytical solution of scattering by local sites has great academic significance to understand physical essence and verify the accuracy of numerical solution. And, it surely has distinct referenced value in practical project.Local hill site is a sort of familiar ground in practical project. Based on this as engineering background, a solution of incident SH waves by an arbitrary shape hill of cross-section.In this thesis, Fourier-Bessel series wave function expansion, auxiliary functions and partition division technique are used to solve this mixed-boundary problem. When considering the quadrature of the ground surface, the paper uses Gaussian quadrature to solve this problem. Numerical solutions are obtained by truncation of the infinite equations and solved by singular value decomposition method.The accuracies of the numerical results are checked up by the convergence of the ground surface displacement and residual errors of boundary conditions with increasing the truncation order. The effects of the shape of the hill, the incident angle, the frequency of the incident waves and the height-to-width ratio of the hill on displacement of ground surface are analyzed. Some beneficial conclusions are given in the end of the thesis.