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刚弹耦合动力学初值问题拟变分原理及其应用

周平 李海波 梁立孚

周平, 李海波, 梁立孚等 . 刚弹耦合动力学初值问题拟变分原理及其应用[J]. 北京航空航天大学学报, 2017, 43(7): 1321-1329. doi: 10.13700/j.bh.1001-5965.2016.0849
引用本文: 周平, 李海波, 梁立孚等 . 刚弹耦合动力学初值问题拟变分原理及其应用[J]. 北京航空航天大学学报, 2017, 43(7): 1321-1329. doi: 10.13700/j.bh.1001-5965.2016.0849
ZHOU Ping, LI Haibo, LIANG Lifuet al. Quasi-variational principle and application of initial value problem for rigid-elastic coupling dynamics[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(7): 1321-1329. doi: 10.13700/j.bh.1001-5965.2016.0849(in Chinese)
Citation: ZHOU Ping, LI Haibo, LIANG Lifuet al. Quasi-variational principle and application of initial value problem for rigid-elastic coupling dynamics[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(7): 1321-1329. doi: 10.13700/j.bh.1001-5965.2016.0849(in Chinese)

刚弹耦合动力学初值问题拟变分原理及其应用

doi: 10.13700/j.bh.1001-5965.2016.0849
基金项目: 

国家自然科学基金 111172046

国家自然科学基金 10272034

详细信息
    作者简介:

    周平 女, 博士, 副教授。主要研究方向:变分原理及其应用

    李海波 男, 博士, 研究员。主要研究方向:航天结构强度与可靠性

    梁立孚 男, 教授, 博士生导师。主要研究方向:变分原理和耦合动力学

    通讯作者:

    梁立孚, E-mail:lianglifu@hrbeu.edu.cn

  • 中图分类号: V414;O313

Quasi-variational principle and application of initial value problem for rigid-elastic coupling dynamics

Funds: 

National Natural Science Foundation of China 111172046

National Natural Science Foundation of China 10272034

More Information
  • 摘要:

    刚弹耦合动力学在国防和民用经济建设中有着广阔的应用前景,但目前还没有完全成熟的理论研究成果。鉴于此,针对刚弹耦合特性,建立初值问题拟变分原理;应用变分方法,推导拟变分原理的拟驻值条件,即得到刚弹耦合动力学的控制方程;给出刚弹耦合动力学初值问题拟变分原理应用的2个算例,1个是应用控制方程求得自由梁的奇数阶振型的解析解,1个是应用变分直接方法Ritz方法求得自由梁的偶数阶振型的解析解。研究表明,刚弹耦合动力学初值问题拟变分原理为建立有限元计算模型提供了依据。

     

  • 图 1  无约束梁自由振动的三阶振型

    Figure 1.  Third-order vibration mode of unrestrained beam in a free vibration

    图 2  无约束梁自由振动的二阶振型

    Figure 2.  Second-order vibration mode of unrestrained beam in a free vibration

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  • 收稿日期:  2016-11-04
  • 录用日期:  2017-01-13
  • 刊出日期:  2017-07-20

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