圆弧状沉积谷地在平面SH波入射下的动力响应

Dynamic response of arc-layered alluvial valley under incidence of plane SH waves

针对圆弧状沉积谷地对平面SH波的二维散射问题,曾有学者提出一种闭合形式的解析解,将波的散射问题转化为一无穷维代数方程组求解,但较高的入射波频率会导致该方程组的系数矩阵病态,从而限制了该解析解适用的频带范围。沿用这种闭合式的解析解的求解思路,并通过选择坐标系避免了线性方程组的求解,散射波函数的待定系数具有明确的解析表达式,因此在一个非常宽的频带范围内给出了该散射问题的解析解,并探讨了入射波与谷地特性对地面运动的影响。

For the two-dimensional scattering problem of plane SH waves in alluvial valley with a circular-arc section, some researchers proposed a type of closed-form analytical solution, which reduced the scattering problem into the solution of an infinite-dimensional algebraic equation system. The high incident frequency will cause the system coefficient matrix to be ill-conditioned, which limits the usable frequency band of the analytical solution. Here, the method of this solution is followed, however, in the solving procedure, the solution of linear equation system is avoided by selecting coordinate system, with the undetermined coefficients of scattering wave functions possessing definite analytical expressions. As a result, the analytical solution to this scattering problem is presented in a very broad frequency band, and the influence of the properties of the incident wave as well as the valley on the ground motion is discussed.