哈密顿体系下机电耦合问题的基本方程

利用多变量变分原理，针对具有机电耦合特性的压电材料，在哈密顿体系下推导出了机电耦合问题的对偶方程．求出了问题的零本征解和非零本征解的一般表达式。并就“二维压电平板对边受均布载荷”这一具体问题进行了完整的分析计算，得出了应力和电位移的具体解答，结果与一般弹性力学所得的结论相吻合，而且精度极高。表明哈密顿体系适用于压电材料的力学分析。

Basic equations of electro-mechanical coupling problem in the Hamiltonian system

To the piezoelectric material with electro-mechanical property, couple equations of electro-mechanical coupling problem in the Hamiltonian system is derived by using the variational principle with multi-variables, and the general expressions of eigenvalue zero and non-zero eigenvalue in the problem are gotten. Full analysis and calculation are made for an idiographic problem that two-dimension piezoelectric slab is subjected to well-distributed load, and exact solutions of stress and electric displacement are obtained, which are consistent with those obtained by the general theory of elasticity and rather precise. The results indicate that the Hamiltonian system is applicable to the mechanics analysis in piezoelectric materials.