波数-频率域内地基土表面位移Green函数的理论分析

建立了柱面坐标系下分层弹性半空间地基土模型。利用钟阳刚度矩阵法和Haskell-Thomson传递矩阵法推导出所有分层土体之间的振动传递关系;根据Helmholtz定理将土体的位移向量分解成势函数的形式,推导出弹性半空间表面应力与位移之间的关系;再将分层土体和半空间地基土通过位移与应力之间的关系进行耦合,得到分层弹性半空间地基土模型表面位移与应力之间的关系。结合单位脉冲荷载作用下地基土表面的边界条件,推导出波数-频率域内地基土表面位移Green函数的解析解,用Matlab程序语言对理论进行实现并通过算例对地基土表面位移Green函数的特征进行了分析和总结。

Analysis of Green's functions in wavenumber-frequency domain for surface displacements of elastic layered half-space soil

The elastic layered half-space soil model is established in the cylindrical coordinates.For layered soil,the vibration transmission relations between the layers are formulated by the Zhong's stiffness matrix method and the Haskell-Thomson transfer matrix method.For half-space soil,the displacement vectors are decomposed as potential functions by the Helmholtz theorem to derive the relationship between the displacement vectors and the stress vectors on soil surface.For layered half-space soil,the upper layered soil is coupled with the bottom half-space soil by the compatibility conditions of the displacement and the stress on their interface,to obtain the transfer matrix between the displacement vector and the stress vector.Combined with the boundary conditions of soil surface under unit impulse excitation,the Green's functions for ground displacements in wavenumber-frequency domain are deduced.The Green's functions obtained are implemented by MATLAB,and their preliminary characteristics are presented via an example.