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多自由度非线性振动系统的内共振

刘世龄 徐兆

刘世龄, 徐兆. 多自由度非线性振动系统的内共振[J]. 应用数学和力学, 1992, 13(1): 27-34.
引用本文: 刘世龄, 徐兆. 多自由度非线性振动系统的内共振[J]. 应用数学和力学, 1992, 13(1): 27-34.
S. L. Lau, Xu Zhao. On Internal Resonance of Nonlinear Vibrating Systems with Many Degrees of Freedom[J]. Applied Mathematics and Mechanics, 1992, 13(1): 27-34.
Citation: S. L. Lau, Xu Zhao. On Internal Resonance of Nonlinear Vibrating Systems with Many Degrees of Freedom[J]. Applied Mathematics and Mechanics, 1992, 13(1): 27-34.

多自由度非线性振动系统的内共振

On Internal Resonance of Nonlinear Vibrating Systems with Many Degrees of Freedom

  • 摘要: 本文研究多自由度非线性自治系统的周期解问题,我们推广了KBM[1]法,本方法可以求得极限环的相图,振幅,周期及其稳定性.
  • [1] Bogoliubov,N.N.,and J.A.Mitropolsky,Asymptotic Methods in the Theory of Nonlinear Vibrations,Moscow,Nauka(1974).
    [2] Navfeh.A.H.,and D.T.Mook.Nonlinear Osciltations,Wiley,New York(1979).
    [3] Mickens,R.E.,A regular perturbation technique for nonlinearly coupled oscillators in resonance,Journal ofSoundand Vibration,81(1982),307-310.
    [4] Sptysl,H.,Internal resonance of non-linear autonomous vibrating system with two degrees of freedom,Journal of Sound and Vibration,112(1987),63-67.
    [5] Xu Zhao and Zhang Ling-qi,Asymptotic method for analysis of non-linear systems with two parameters,Acta Mathematica Scientia,6(1986),453-462.
    [6] Pavlidis,T.,Biological Oscillators:Their Mathematical Analysis,Academic Press,New York(1973).
    [7] Rand,R.H.,and P.J.Holmes,Bifurcation of periodic motions in two weakly coupled van der Poi oscillators,Int.J.Non-Linear Mechanics,15(1980),387-399.
    [8] Lau.S.L.,Y.K.Cheung and S.Y.Wu,A variable parameter incrementation method for dynamic instability of linear and nonlinear elastic systems,ASME.J.Appl.Mech.,49(1982),849-853.
    [9] Xu Jian-xue,R.S.Guttalu,and C.S.Hsu,Domains of attraction for multiple limit cycles of coupled van der Poi equations by simple cell mappings,Int.J.Non-Linear Mech.,20(1985),507-517.
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  • 刊出日期:  1992-01-15

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