求解层状轴对称课题的传递矩阵法

Transfer matrix method to solve axisymmetrical multilayered problems using

总结了求解轴对称层状半无限体的传递矩阵法 ,认为静态弹性、静态粘弹性、动态弹性和动态粘弹性轴对称层状半无限体都可以用统一的状态方程来描述 ,参照现代控制论中求解状态方程的方法 ,解出上述方程组 ,然后针对半无限体特殊的边界情况进行了处理 ,并以动态问题为例 ,给出动态传递矩阵的具体表达式及已知表面状态向量时的应力、位移表达式 ,最后给出了传递矩阵的几点性质。

To solve axisymmetrical multilayered half space problems, a new unified state equation is presented in this paper, which can describe the static elastic, static viscoelastic, dynamic elastic and dynamic viscoelastic models. The state equation group is solved with method of modern control theory. Several characteristics of transfer matrix are presented. Finally the dynamic transfer matrix is given as an example.