In this paper, a model of transversely isotropic elastic strata is used to simulate the soil layers situated on a half space. Instead of the half space, an artificial transmitting boundary is used to absorb the vibration energy. The displacement formulas at any soil layer interface under vertical or horizontal harmonic ring loads are obtained by using the thin layer element method. From these formulas, the explicit solutions of Green's functions-the displacement responses at any interface of these strata under vertical and horizon harmonic point loads- are derived. The examples show that the method presented in this paper is close to the theoretical method and the transversely isotropic property has evident influence on the Green's functions.

运用广义Fourier级数方法推导了无约束平面框架结构受运动刚体冲击时的瞬态动力响应公式，利用这些公式得到冲击系统动力响应解析解，在公式推导过程中得出结构系统中弹性响应的动量之和为零的结论，从公式推导可以看出,模态分析法同样可以用来解决此类冲击问题。