Scattering Of Plane SH Wave By A Semi-elliptical Hill: Semi-analytical Solution

Site response problems are always 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 obviously, resulting in the sensitive changes of the ground surface, underground structures and buildings in a narrow special scale, furthermore, influencing the distribution of earthquake damage.Therefore, the research of analytical solution on scattering by local sites has great academic significance to understand physical nature and verify the accuracy of numerical solution, certainly, providing distinct reference value in practical projects. Local hill is a sort of rather common site in practical project and its amplifying effect on buildings constructed around this kind of site should be considered properly. However, the past efforts focus mainly on those simplified by circular outline although the elliptical shape can simulate the nature condition better. Based on this engineering background, a semi-analytical solution of incident SH wave by a elliptical hill is discussed.In order to fit the terrain condition, this dissertation uses Mathieu function and modified Mathieu function during the process of wave function expansion, also tries two different methods in small elliptical hill and high elliptical hill to overcome the barrier of composite boundary condition.At last, the dissertation analyzes the problems in these two methods and gives some advice on construction design in local sites.