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一类碰撞振动系统的余维二分叉和Hopf分叉*

谢建华

谢建华. 一类碰撞振动系统的余维二分叉和Hopf分叉*[J]. 应用数学和力学, 1996, 17(1): 63-73.
引用本文: 谢建华. 一类碰撞振动系统的余维二分叉和Hopf分叉*[J]. 应用数学和力学, 1996, 17(1): 63-73.
Xie Jianhua. Codimension Two Bifurcations and Hopf Bifurcations of an Impacting Vibrating System[J]. Applied Mathematics and Mechanics, 1996, 17(1): 63-73.
Citation: Xie Jianhua. Codimension Two Bifurcations and Hopf Bifurcations of an Impacting Vibrating System[J]. Applied Mathematics and Mechanics, 1996, 17(1): 63-73.

一类碰撞振动系统的余维二分叉和Hopf分叉*

基金项目: * 国家自然科学基金

Codimension Two Bifurcations and Hopf Bifurcations of an Impacting Vibrating System

  • 摘要: 本文研究弹簧质量系统对无穷大平面碰撞振动的分叉问题。证明了在接近完全弹性碰撞和在一些特殊的频率比附近,存在余维二分叉现象。利用映射的正则型理论,将Poincaré映射变换成含两个参数的正则型,通过分析该正则型,我们得到周期倍化分叉、周期1点、2点的Hopf分叉。并进行了数值验证。
  • [1] S. W. Shaw and P. L. Holmes, A periodically forced piece-wise linear oscillator, Journal of Sound and Vibration, 90,1 (1983), 129-155.
    [2] P. C. Tung and S. W. Shaw, The dynamics of an impact print hammer, Journal of Vibration, Acoustics, Stress and Reliability in Design, 110, 4(i988), 193-199.
    [3] J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcation of Vector Fields, New York:Springer-Verlag(1983),102-116.
    [4] Shu Zhdngzhou, Motion types and chaos of multi-body systems vibrating with impacts, Acta Mechanica Sinica, 7. 4 (1991). 369-375.
    [5] H. Ishihana, Y. Takagi and S. Maezawa, Analysis of impact vibration to deltafunction method-care of one degree-of-freedom system, first report: prefectly elastic collision, 20th Japan Nat. Congress for Applied Mechanics, Tokyo (1970).
    [6] 谢建华.冲击式振动落砂机分叉问题研究,全国第三届运动稳定性与振动学术会议论文集:K运动稳定性、振动、分叉与混沌的研究》,中国科学技术出版社,北京(1992).
    [7] O. E. Lanford, Bifurcation of periodic solution into invariant tori: The work of Ruelle and Takens, Lecture Notes in Math., 322, Berlin-Heidelberg, New York, Springer-Verlag (1973).
    [8] Y. H. Wan, Computation of the stabity condition for the Hopf bifurcation of diffeomorphisms on R2, SIAM, J. Appl. Math., 34, 1 (1978).
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出版历程
  • 收稿日期:  1994-10-05
  • 刊出日期:  1996-01-15

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