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

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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。

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	周平
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关键词 ：刚弹耦合动力学, 初值问题, 拟变分原理, 控制方程, 自由梁

Abstract：The rigid-elastic coupling dynamics has been widely used in the national defense and civil economic construction, but there are still no mature theoretical research results. In this view, the quasi-variational principle of the initial value problem was established, according to rigid-elastic coupling characters, and the quasi-stationary condition of the quasi-variational principle was derived by the variational method. This condition is the governing equation of rigid-elastic coupling dynamics. Two examples were given to show the application of this condition. One was the analytical solution of the odd order vibration mode of free beam obtained by the governing equation. The other is the analytical solution of the even order vibration mode of the free beam obtained by the variational direct method Ritz method. The results show that the quasi-variational principle of the initial value problem of the rigid-elastic coupling dynamics provides the basis for the establishment of finite element model.

Key words： rigid-elastic coupling dynamics initial value problem quasi-variational principle governing equation free beam

收稿日期: 2016-11-04 出版日期: 2017-02-22

PACS:	V414
	O313

基金资助:国家自然科学基金（111172046，10272034）

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

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。

引用本文:

周平, 李海波, 梁立孚. 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.
ZHOU Ping, LI Haibo, LIANG Lifu. Quasi-variational principle and application of initial value problem for rigid-elastic coupling dynamics. JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2017, 43(7): 1321-1329.

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http://bhxb.buaa.edu.cn/CN/10.13700/j.bh.1001-5965.2016.0849 或 http://bhxb.buaa.edu.cn/CN/Y2017/V43/I7/1321

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