层状弹性半空间非轴对称动力问题的奇异解

在柱坐标系下，利用关于方位角的Ｆｏｕｒｉｅｒ变换及关于径向的Ｈａｎｋｅｌ变换，将弹性力学基本方程组转化为非齐次的一阶常微分方程组的标准形式．采用求解微分方程组的矩阵法，建立了介质层的传递矩阵．由层间完全接触条件，导出了在任意埋藏源作用下层状弹性半空间频域奇异解，时域奇异解可通过关于频率的Ｆｏｕｒｉｅｒ积分得到．该方法可应用到固体、流体层的情况

SINGULAR SOLUTIONS OF NON-AXISYMMETRIC DYNAMIC PROBLEM IN LAYERED ELASTIC HALF-SPACE

The Fourier transformations about the azimuthal angle and Hankel transformation about the radial direction have been used to convert the basic equations of elasticity into a non-homogenous first-order ordinary differential equation system in cylindrical coordinates. By the use of the matrix method to solve this system of equations, the transmission matrices of the layered medium are established. The singular solution in frequency domain for an arbitrarilly buried source acting in the multilayered elastic half-space is obtained by Fourier synthesis over frequency. The presented method can be applied to solid and fluid layers.