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非线性颤振系统中既是超临界又是亚临界的Hopf分岔点研究

陈衍茂 刘济科

陈衍茂, 刘济科. 非线性颤振系统中既是超临界又是亚临界的Hopf分岔点研究[J]. 应用数学和力学, 2008, 29(2): 181-187.
引用本文: 陈衍茂, 刘济科. 非线性颤振系统中既是超临界又是亚临界的Hopf分岔点研究[J]. 应用数学和力学, 2008, 29(2): 181-187.
CHEN Yan-mao, LIU Ji-ke. Supercritical as Well as Subcritical Hopf Bifurcation in Nonlinear Flutter Systems[J]. Applied Mathematics and Mechanics, 2008, 29(2): 181-187.
Citation: CHEN Yan-mao, LIU Ji-ke. Supercritical as Well as Subcritical Hopf Bifurcation in Nonlinear Flutter Systems[J]. Applied Mathematics and Mechanics, 2008, 29(2): 181-187.

非线性颤振系统中既是超临界又是亚临界的Hopf分岔点研究

基金项目: 国家自然科学基金资助项目(10772202);教育部博士学科点专项基金资助项目(20050558032);广东省自然科学基金资助项目(07003680;05003295)
详细信息
    作者简介:

    陈衍茂(1982- ),男,江西兴国人,博士生;刘济科,教授,博士(联系人.Tel:+86-20-84114666;E-mail:jikeliu@hotmail.com).

  • 中图分类号: O345;O322

Supercritical as Well as Subcritical Hopf Bifurcation in Nonlinear Flutter Systems

  • 摘要: 研究了二元机翼非线性颤振系统的Hopf分岔.应用中心流形定理将系统降维,并利用复数正规形方法得到了以气流速度为分岔参数的分岔方程.研究发现,分岔方程中一个系数不含分岔参数的一次幂,故使得分岔具有超临界和亚临界双重性质.用等效线性化法和增量谐波平衡法验证了所得结果.
  • [1] Lee B H K, Price S J,Wong Y S.Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos[J].Progress Aerosp Sci,1999,35(3):205-344. doi: 10.1016/S0376-0421(98)00015-3
    [2] Liu J K, Zhao L C. Bifurcation analysis of airfoil in incompressible flow [J].J Sound Vibration,1992,154(1):117-124. doi: 10.1016/0022-460X(92)90407-O
    [3] Shahrzad P, Mahzoon M. Limit cycle flutter of airfoils in steady and unsteady flows[J].J Sound Vibration,2002,256(2):213-225. doi: 10.1006/jsvi.2001.4113
    [4] Yang Y R. KBM method of analyzing limit cycle flutter of a wing with an external store and comparison with wind tunnel test[J].J Sound Vibration,1995,187(2):271-280. doi: 10.1006/jsvi.1995.0520
    [5] Liu L P, Dowell E H.The secondary bifurcation of an aeroelastic airfoil motion: effect of high harmonics[J].Nonlinear Dyn,2004,37(1):31-49. doi: 10.1023/B:NODY.0000040033.85421.4d
    [6] 蔡铭,刘济科,李军. 多自由度强非线性颤振分析的增量谐波平衡法[J].应用数学和力学,2006,27(7):833-838.
    [7] Kousen K A, Bendiksen O O. Limit cycle phenomena in computational transonic aeroelasticity[J].J Aircraft,1994,31(6):1257-1263. doi: 10.2514/3.46644
    [8] Liu J K, Zhao L C, Fang T. Bifurcation point analysis of airfoil flutter with structural nonlinearity[A].In:HUANG Wen-hu,Ed.Advances in Nonlinear Dynamics in China—Theory and Practice[C].Chapter 3. Lisse,the Netherland: Swets & Zeitlinger Publishers, 2002.
    [9] Lee B H K, Gong L, Wong Y S. Analysis and computation of nonlinear dynamic response of a two-degree-of-freedom system and its application in aeroelasticity[J].J Fluids Struct,1997,11(3):225-246. doi: 10.1006/jfls.1996.0075
    [10] Liu L, Wong Y S,Lee B H K. Application of the center manifold theory in nonlinear aeroelasticity[J].J Sound Vibration,2000,234(4):641-659. doi: 10.1006/jsvi.1999.2895
    [11] Coller B D, Chamara P A. Structural non-linearities and the nature of the classic flutter instability[J].J Sound Vibration,2004,277(4/5):711-739. doi: 10.1016/j.jsv.2003.09.017
    [12] 毕勤胜, 陈予恕.双摆内共振分叉分析[J].应用数学和力学,2000,21(3):226-234.
    [13] 叶瑞松.一种计算Hopf 分歧点的新方法[J]. 应用数学和力学,2000,21(11):1172-1178.
    [14] 魏俊杰, 张春蕊,李秀玲.具时滞的二维神经网络模型的分支[J].应用数学和力学,2005,26(2):193-200.
    [15] Guckenheimer J,Holmes P.Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields[M].New York: Springer-Verlag, 1983.
    [16] Carr J.Applications of Center Manifold Theory[M].New York: Springer-Verlag;Berlin: Heidelberg, 1981.
    [17] Leung A Y T, Zhang Q C. Complex normal form for strongly nonlinear vibration systems exemplified by Duffing-Van der Pol equation[J].J Sound Vibration,1997,213(5):907-914.
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出版历程
  • 收稿日期:  2007-08-15
  • 修回日期:  2008-01-03
  • 刊出日期:  2008-02-15

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