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力学与实践 ›› 2004, Vol. 26 ›› Issue (2): 0-0.doi: 10.6052/1000-0992-2003-040

• 应用研究 •    

Melnikov 方法在输流管混沌运动研究中的应用

邹光胜 金基铎 闻邦椿   

  1. 沈阳市东北大学机械工程与自动化学院 110004 沈阳市东北大学机械工程与自动化学院 110004 沈阳东北大学机械工程与自动化学院
  • 收稿日期:2003-02-05 修回日期:2003-05-22 出版日期:2004-04-10 发布日期:2004-04-10

APPLICATION OF MELNIKOV METHOD IN THE STUDY OF CHAOTIC MOTIONS OF PIPE CONVEYING FLUID

  • Received:2003-02-05 Revised:2003-05-22 Online:2004-04-10 Published:2004-04-10

摘要: 对基础简谐运动激励下两端固定输流管道的混沌运动进行了研究. 推导出了系统 的运动方程,确定了系统存在的平衡点及其稳定性,计算出了未扰系统的同宿轨道,并利用 Melnikov方法得到了系统发生混沌运动时参数需满足的临界条件,同时还利用相平面图和 Poinc\'are映射等方法对管道的混沌运动进行了数值模拟. 通过比较发现,由Melnikov 方法确定的临界参数值要稍小于数值模拟中首次观察到混沌运动时对应的临界值.

关键词: Melnikov 方法, 输流管, 混沌运动, 数值模拟

Abstract: The chaotic vibrations of a clamped-clamped pipe conveying fluid, excited by the harmonic motions of its supporting base, were investigated theoretically. The nonlinear equations of motion were derived, and the equilibrium and stabilities of the system were analyzed. The expressions of homoclinic orbits of the unperturbed system were calculated. The system parameters for the occurrence of chaotic motions were obtained by means of Melnikov method. Phase portrait and Poinc\'are map were used to simulate the chaotic motions of the original system. Comparison between the results from theoretical analyses and numerical simulations reveals that the critical value of the parameter determined by Melnikov method is slightly lower than that corresponding to the chaotic motion observed first in numerical simulations.

Key words: Melnikov method, pipe conveying fluid, chaotic motion,