半空间饱和土在内部简谐水平力作用下的Green函数

摘要

By using integral transform method, Green functions of horizontal harmonic force applied to the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above-mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, Green functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.%根据积分变换方法得出了半空间内部作用简谐水平力时的Green函数．首先，利用Hankel积分变换方法，直接对频域内的Biot波动方程进行求解，得出Biot波动方程的通解；利用通解和半空间内部作用水平力时边界上的边界条件，以及力作用面上的连续性条件，可以得出上述边值问题的解；对于边值问题在变换域内的解进行相应的逆变换，就可以得出频域内的Green函数．本文得到的线弹性退化解与文献中的结果吻合．最后，文中给出了两个算例．