›› 2014, Vol. 36 ›› Issue (3): 337-340.DOI: 10.6052/1000-0879-13-085

• 应用研究 • 上一篇    下一篇

自由端受水平冲击后悬链的运动分析

肖越, 曾凡林   

  1. 哈尔滨工业大学航天科学与力学系, 哈尔滨150001
  • 收稿日期:2013-03-22 修回日期:2013-05-16 出版日期:2014-06-08 发布日期:2014-06-10
  • 通讯作者: 曾凡林,E-mail:zengfanlin@hit.edu.cn

MOTION OF A HANGING CHAIN AFTER AN INITIAL HORIZONTAL IMPACT AT THE FREE END

XIAO Yue, ZENG Fanlin   

  1. Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin 150001, China
  • Received:2013-03-22 Revised:2013-05-16 Online:2014-06-08 Published:2014-06-10

摘要: 悬链在自由端受到冲击后的瞬态响应,不仅是一个有趣的数学问题,同时也具有一定的工程意义.在拉格朗日动力学微分方程的理论框架下,引入广义冲量并利用第二类拉格朗日方程对悬链在自由端受水平冲击力后的动力学响应进行了分析,得到了计算每节链段角速度的统一公式. 应用该公式能够方便地求解不同初始条件下具有较多链段数目的悬链在冲击作用下的瞬态响应问题.

关键词: 悬链|拉格朗日方程|广义冲量|瞬态响应

Abstract: The transient response of a hanging chain after an initial impact at the free end, is not only an interesting mathematical problem, but also has a certain engineering application. In the theoretical frame of the Lagrange dynamics differential equation, the dynamic response of a hanging chain under the impact of a horizontal impulse-momentum S is analyzed by using the second kind Lagrange's equations under a generalized impulse-momentum, and a general solution is obtained to compute the angular velocity of each segment. This method can be used conveniently to obtain the transient response of a hanging chain with several segments and in different initial conditions.

Key words: hanging chain|Lagrange equations|generalized impulse-momentum|transient response

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