矩形中厚板自由振动问题的哈密顿体系与辛几何解法

以矩形中厚板的胡海昌方程为基础，将中厚板自由振动问题导入哈密顿体系，然后利用辛几何中的分离变量和本征函数展开的方法求出了对边简支板自由振动的精确解．文中采用的辛方法不必事先人为地引入试函数，而是通过完全理性的推导，从而突破了传统半逆解法的限制，使得问题的求解更加合理，易于推广．计算实例证明了本文推导结果的正确性．

On hamilton system and new symplectic approach for free vibration of moderately thick rectangular plates

Based on Hu's equations of moderately thick rectangular plates,the free vibration problem for the plates were transferred into Hamilton system. Then,the whole state variables were separated. Using the method of eigenfunction expansion in the symplectic geometry,the exact free vibration solutions of the plates with two opposite sides simply supported were obtained. Since only the basic elasticity equations of the plates were used,the method eliminates the need to pre-determine any trial functions and is henc...