利用结构力学与最优控制的模拟理论 ,研究弹性波在层状介质中传播的数值计算方法 .将弹性波传播问题导向哈密顿 (Hamilton)体系 ,在哈密顿体系中 ,推导出一种新的半解析单元 ,称之为动力 -部分杂交元 ,由此导出一套哈密顿体系下的半解析数值计算方法 .本文给出了该方法在层状正交各向异性材料介质的弹性波传播问题的数值算例 ,分析了一定频率的弹性波在层状介质中传播时的位移、应力的模式 .计算结果展现了Hamilton体系和辛几何在弹性波传播问题研究的应用前景 . Based on the simulation theory of structural mechanics and optimal control, a numerical method of elastic wave propagation in layered media is studied. The elastic wave propagation problem is directed to Hamiltonian system, and a new kind of Hamiltonian system is derived Semi-analytical unit, which is called dynamic-partial hybrid element, thus a set of semi-analytical numerical method is deduced under the Hamiltonian system.In this paper, the problem of elastic wave propagation in layered orthotropic materials , The displacement and stress modes of the elastic waves propagating in a layered medium with a certain frequency are analyzed.The calculation results show the application prospect of Hamiltonian system and symplectic geometry in the study of elastic wave propagation.