CHEN Yu-shu, YANG Cai-xia, WU Zhi-qiang, CHEN Fang-qi. 1:2 Internal Resonance of Coupled Dynamic System With Quadratic and Cubic Nonlinearities[J]. Applied Mathematics and Mechanics, 2001, 22(8): 817-824.
Citation: CHEN Yu-shu, YANG Cai-xia, WU Zhi-qiang, CHEN Fang-qi. 1:2 Internal Resonance of Coupled Dynamic System With Quadratic and Cubic Nonlinearities[J]. Applied Mathematics and Mechanics, 2001, 22(8): 817-824.

1:2 Internal Resonance of Coupled Dynamic System With Quadratic and Cubic Nonlinearities

  • Received Date: 2000-05-08
  • Rev Recd Date: 2001-03-15
  • Publish Date: 2001-08-15
  • The 1:2 internal resonance of coupled dynamic system with quadratic and cubic nonlinearities is studied.The normal forms of this system in 1:2 internal resonance were derived by using the direct method of normal form.In the normal forms,quadratic and cubic nonlinearities were remained.Based on a new convenient transformation technique,the 4-dimension bifurcation equations were reduced to 3-dimension.A bifurcation equation with one-dimension was obtained.Then the bi furcation behaviors of a universal unfolding were studied by using the singularity theory.The method of this paper can be applied to analyze the bifurcation behavior in strong internal resonance on 4-dimension center manifolds.
  • loading
  • [1]
    Nayfeb A H,Mook D T.Nonlinear Oscillations[M].New York:John Wiley & Sons,1979.
    [2]
    Langford W F,Zhan K,Dynamics of 1/1 resonance in vortex-induced vibration[A].In:M P Paidoussis Ed.ASME Fundmental Aspects of Fluid Structure Interactions[C].PVP-Vol.247,Book,No G00728-1992.
    [3]
    Leblanc V G,Langford W F.Classification and unfoldings of 1:2 resonant Hopf bifurcation[J].Arch Rational Mech Anal,1996,(136):305-357.
    [4]
    吴志强.多自由度非线性系统的非线性模态及Normal Form直接方法[D].博士论文,天津:天津大学,1996.
    [5]
    陈芳启,吴志强,陈予恕.一类粘弹性圆柱壳的高余维分岔[J].力学学报,2001,33(3):286-293.
    [6]
    陈予恕,杨彩霞.一类刚柔耦合非线性系统的动力学建模[J].中国空间科学技术,2000(3):712.
    [7]
    CHEN Yu-shu,Leung A Y T.Bifurcation and Chaos in Engineering[M].London:Springer-Verlag,1998.
    [8]
    陆启韶.分岔与奇异性[M].上海:上海科技教育出版社,1995.
    [9]
    陈予恕.非线性振动系统的分岔和混沌理论[M].北京:高等教育出版社,1993.
    [10]
    陆启韶.常微分方程定性理论与几何方法[M].北京:北京航空航天大学出版社,1988.
    [11]
    Arnold V I.Geometrical Methods in the Theory of Or dinary Differential Equations[M].2nd ed.New York:Springer-Verlag,1988.
    [12]
    Golubitsky M,Schaeffer D G.Singularities and Bifurcation Theory,Vol.1[M].New York:Springer-Verlag,1985.
    [13]
    Chow S N,Hale S.Methods of Bifur cation Theory[M].New York:Springer-Verlag,1992.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2317) PDF downloads(650) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return