Ji Jinchen, Chen Yushu. Bifurcation in a Parametrically Excited Two-Degree-of-Freedom Nonlinear Oscillating System with 1:2 Internal Resonance[J]. Applied Mathematics and Mechanics, 1999, 20(4): 337-345.
Citation: Ji Jinchen, Chen Yushu. Bifurcation in a Parametrically Excited Two-Degree-of-Freedom Nonlinear Oscillating System with 1:2 Internal Resonance[J]. Applied Mathematics and Mechanics, 1999, 20(4): 337-345.

Bifurcation in a Parametrically Excited Two-Degree-of-Freedom Nonlinear Oscillating System with 1:2 Internal Resonance

  • Received Date: 1998-01-06
  • Rev Recd Date: 1998-09-02
  • Publish Date: 1999-04-15
  • The nonlinear response of a two-degree-of-freedom nonlinear oscillating system to parametric excitation is examined for the case of 1:2 internal resonance and,principal parametric resonance with respect to the lower mode.The method of multiple scales is used to derive four first-order autonomous ordinary differential equations for the modulation of the amplitudes and phases.The steady-state solutions of the modulated equations and their stability are investigated.The trivial solutions lose their stability through pitchfork bifurcation giving rise to coupled mode solutions.The Melnikov method is used to study the global bifurcation behavior,the critical parameter is determined at which the dynamical system possesses a Smale horseshoe type of chaos.
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  • [1]
    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.
    [2]
    Nayfeh A H,Nayfeh J F.Surface waves in closed basins under principal and autoparametric resonances[J].Phys Fluids,1990,A2(9):1635~1648.
    [3]
    Feng Z C,Sethna P R.Global bifurcation and chaos in parametrically forced systems with one-one resonance[J].Dynamics and Stability of Systems,1990,5(4):210~225.
    [4]
    Feng Z C,Wiggins S.On the existence of chaos in a class of two-degree-of-fredom,damped,strongly parametrically forced mechanical systems with broken O(2) symmetry[J].Z Angew Math Phys,1993,44(2):201~248.
    [5]
    Nayfeh A H.Perturbation Methods[M].New York:Wiley-Interscience,1973.
    [6]
    Wiggins S.Global Bifurcations and Chaos——Analytical Methods[M].New York:Springer-Verlag,1990.
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