Hamilton体系及弹性波在层状介质中的传播问题

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.

HAMILTONIAN SYSTEM AND ELASTIC WAVE PROPAGATION IN LAYERED MEDIA

Based on the analogy of structural mechanics and optimal control, the theory of Hamiltonian system can be introduced into elastic wave guide problems. In Hamiltonian system, a new type of semi analytical element is derived, which is called dynamic partial hybrid element, and is deduced via substitution of variables and the variational principle. Thus, a semi analytical finite element method （FEM） in Hamiltonian system can be founded. The numerical results of wave propagation in layered media in a strip domain are present, and the displacement and stress modes for a definite frequency are analyzed. The numerical results demonstrate the broad prospect of this method.