| 膜自由振动的多辛方法 |
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| 引用本文： | 胡伟鹏,邓子辰,李文成. 膜自由振动的多辛方法[J]. 应用数学和力学, 2007, 28(9): 1054-1062 |
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| 作者姓名： | 胡伟鹏 邓子辰 李文成 |
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| 作者单位： | 西北工业大学 力学与土木建筑学院,西安 710072;2.大连理工大学 工业装备结构分析国家重点实验室,辽宁 大连 116023;3.西北工业大学 理学院,西安 710072 |
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| 基金项目： | 国家自然科学基金;教育部跨世纪优秀人才培养计划;国家重点实验室基金 |
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| 摘 要： | 基于Hamilton空间体系的多辛理论研究了膜自由振动问题，讨论了构造复合离散多辛格式的方法，并构造了一种典型的9×3点半隐式的多辛复合离散格式，该格式满足多辛守恒律、能量守恒律和动量守恒律．数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性．
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| 关 键 词： | 多辛 复合离散 Runge-Kutta方法 |
| 文章编号： | 1000-0887（2007）09-1054-09 |
| 收稿时间： | 2007-01-18 |
| 修稿时间： | 2007-01-18 |
Multi-Symplectic Methods for Membrane Free Vibration Equation |
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| HU Wei-peng,DENG Zi-chen,LI Wen-cheng. Multi-Symplectic Methods for Membrane Free Vibration Equation[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1054-1062 |
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| Authors: | HU Wei-peng DENG Zi-chen LI Wen-cheng |
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| Affiliation: | School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnincal University, Xi'an 710072, P. R. China; |
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| Abstract: | The multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space were considered.The complex method was introduced and a semi-implicit twenty-seven-point scheme with certain discrete conservation laws-a multi-symplectic conservation law(CLS),an energy conservation law(ECL) as well as a momentum conservation law(MCL)-is constructed to discrete the PDEs that are derived from the membrane free vibration equation.The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior. |
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| Keywords: | multi-symplectic complex discretization Runge-Kutta method |
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