中文摘要：

研究弹性波散射与多重散射的T矩阵方法。首先，基于Helmholtz体内和体外公式推导了对应于圆柱型散射体的T矩阵元素的具体表达式；接着分析了在含多个随机分布圆柱型散射体的随机非均匀介质中弹性波的多重散射并给出在统计平均意义下的相干波的定义以及波速和衰减系数计算公式；最后，针对Ge／Al、Sic／At复合材料用Matlab进行了编程和数值计算；计算单个柱型散射体的散射截面以及随机非均匀介质中相干波的速度和衰减系数，分析了这种介质的频散特性。

英文摘要：

The T matrix method used for single and multiple scattering of elastic waves is studied in this paper. Firstly, the specific expressions of elements in the T matrix for circular cylinder are derived from the interior and exterior Helmholtz equations. Next, the multiple scattering in the random medium with random distributed parallel circular cylinders is analyzed. The definition of coherent waves with statistical average viewpoint and the equations to estimate the velocities and attenuation of coherent waves are given. At last, the numerical computation is carried out for composite Ge/A1 and SiC/A1. The scattering cross-section of a cylinder and the velocity and attenuation of coherent waves propagating through a random inhomogeneous medium are computed. The dispersive characteristics of coherent waves in random medium are discussed.