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| 四边固支矩形薄板自由振动的哈密顿解析解 | |
| 引用本文： | 钟阳,李锐,田斌. 四边固支矩形薄板自由振动的哈密顿解析解[J]. 应用力学学报, 2011, 28(4) |
| 作者姓名： | 钟阳 李锐 田斌 |
| 作者单位： | 大连理工大学,大连,116024 |
| 基金项目： | 科学技术部重大基础研究项目(2004CCA03300) |
| 摘 要： | 在哈密顿体系中利用辛几何方法求解了四边固支矩形薄板自由振动问题的解析解。首先,从基本方程出发,将问题表示成Hamilton正则方程,然后利用辛几何方法导出本征值问题,从而得到本征函数解,使之满足边界条件;再由方程组有非零解的条件,最终推导出四边固支矩形薄板的自振频率方程,得到频率的解析解。计算了不同长宽比情况下四边固支矩形薄板的频率,结果与已有文献完全一致。该解法有望推广至更多尚未得到解析解的矩形板的振动问题。 |
| 关 键 词： | 固支矩形薄板 解析解 Hamilton体系 辛几何方法 |
Analytic free vibration solution of fully clamped rectangular thin plate |
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| Zhong Yang Li Rui Tian Bin. Analytic free vibration solution of fully clamped rectangular thin plate[J]. Chinese Journal of Applied Mechanics, 2011, 28(4) | |
| Authors: | Zhong Yang Li Rui Tian Bin |
| Affiliation: | Zhong Yang Li Rui Tian Bin(Faculty of Infrastructure Engineering,Dalian University of Technology,116024,Dalian,China) |
| Abstract: | The analytic free vibration solution of fully clamped rectangular thin plate is derived by the symplectic geometry approach in Hamiltonian system.The basic equations for rectangular thin plate are first transferred into Hamilton canonical equations.Using the symplectic geometry method yields the eigenvalue problem then the eigen solution is obtained.The boundary conditions of fully clamped rectangular thin plate are satisfied so as to give the frequency equations.Then,the analytic solution is obtained.Numer... |
| Keywords: | clamped rectangular thin plate analytic solution Hamiltonian system symplectic geometry method |
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