圆弧状凹陷地形在平面SH波入射下的动力响应:高频解答

Dynamic Response of Circular-arc-shaped Canyon under the Incidence of Plane SH Wave:High-frequency Solution

利用波函数的Fourier-Bessel级数展开法和外域型Graf加法公式,推导了圆弧状凹陷地形对平面SH波二维散射问题的解析解。与现有其他解析解不同的是,该解析解的获得无须求解线性方程组,从而避免了高频波入射下方程组系数矩阵可能出现的病态问题。因此,既使在入射波频率很高的情况下,该解析解也能够收敛。利用该解,在一个非常宽的频带范围内讨论了凹陷地形的几何形状对地面运动的影响。

Using Fourier-Bessel series expansion of wave functions and the exterior Graf＇s addition formula, the analytical solution to the two-dimension scattering problem of SH waves by the circular-arc-shaped canyon topography is deducted. Compared to other analytical solutions available so far, the acquisition of our solution does not need solve linear equation system, which avoids the possible ill-conditioned issues that might arise in the coefficient matrix of the equation system for the cases of the incident waves with high frequencies. Therefore, even for very high frequencies of incident waves, the proposed analytical solution can still converge. Using the deducted solution, the influence, which is imposed by the geometries of the canyon topography on the ground motion, is discussed in very broad frequency band.