【作者】 杨宇；

【导师】 梁建文；

【作者基本信息】 天津大学 ， 结构工程， 2005， 硕士

【摘要】 场地反应问题是地震工程学中的一类重要的波动问题。大量地震震害表明,局部地形的存在对地震波的散射有很大的影响,从而造成场地地表、地下结构或地上建筑的震害反应在很小的范围内即有很大的变化,进而影响震害的分布。因此对此类问题的求解,在理论上和工程应用上都有重要的意义。楔形地形是工程中常见的一类场地。本文对平面SH波入射和平面P波入射分别进行了研究,采用的是Fourier-Bessel级数展开法,采用大圆弧假定用两个大圆弧来模拟自由表面,用Graf公式进行坐标变换,根据边界条件求解未知数,从而得到楔形地形的地表位移。本文定性分析了地形角度、入射角度和入射频率等因素的影响,并从级数项数增加时地表位移结果的收敛以及边界条件残量的收敛两个方面验证了结果的正确性。研究结果表明,不论是平面SH波还是平面P波入射,在楔形顶点附近位移幅值都有放大,放大倍数根据不同的地形和不同的入射角度不同。更多还原

【Abstract】 Site response problem is one of the most important subjects inearthquake engineering. A lot of investigations of earthquake damage showthat the existence of local sites affects the scattering and diffraction ofseismic wave greatly. Hence, there is sensitive variation of earthquakeresponse of ground surface, underground structure and buildings in narrowspatial dimension. Therefore, the investigation of this kind of problem hasimportant meaning on both theory research and practical project.Wedge site is a sort of common topography in practical project. Westudy plane SH-Waves and plane P-Waves in this thesis. Fourier-Besselseries expansion is used to solve the problem. Two very big circles are usedto simulate the free boundary and Graf’s addition theorem is used to convertthe coordinates. Finally, the unknowns are resolved on the basis of theboundary conditions and the surface displacement is obtained.The effect of parameters such as the wedge angle, the incident wavefrequency and the angle of incidence is also analyzed. Furthermore, theaccuracies of the numerical results are checked by the convergence of theground surface displacement and residual errors of boundary conditionswith the increasing progression term. The results demonstrate that theamplification of incident wave almost occurs around the vertex of thewedge due to plane SH-Waves or P-Waves. The degree of amplification isvariable with the wedge angle and incident angle.更多还原