Scattering of Plane SH-Wave by a Cylindrical Hill of Arbitrary Shape
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摘要: 将具有任意形状的凸起地形对稳态SH波散射问题转换为契合问题加以研究。利用求解弹性波动问题的复变函数与保角映射方法,在包括任意形状凸起边界在内的一个区域中,构造一个在凸起边界上应力自由,其他部分位移和应力均为任意的驻波解。然后再将这个驻波解与其余下的区域中的散射波解在两个区域结合面上完成契合过程,由此决定出这两个区域中的驻波和散射波解答。最后对圆弧形和半椭圆形凸起进行了数值计算,并将计算结果与有限元法的数值解进行了比较。Abstract: The problems of scattering of plane SH-wave by a cylindrical hill of arbitrary shape is studied based on the methods of conjunction and division of solution zone. The scattering wave function is given by using the complex variable and conformal mapping methods. The conjunction boundary conditions are satisfied. Further more appling orthogonal function expanding technique, the problems can finally be summarized into the solution of a series of infinite algebraic equations. At last, numerical results of surface displacements of a cylindrical arc hill and of a semi-ellipse hill are obtained. And those computational results are compared with the results of finite element method(FEM).
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