TANG Jia-shi. The MLP Method for Subharmonic and Ultraharmonic Resonance Solutions of Strongly Nonlinear Systems[J]. Applied Mathematics and Mechanics, 2000, 21(10): 1039-1045.
Citation: TANG Jia-shi. The MLP Method for Subharmonic and Ultraharmonic Resonance Solutions of Strongly Nonlinear Systems[J]. Applied Mathematics and Mechanics, 2000, 21(10): 1039-1045.

The MLP Method for Subharmonic and Ultraharmonic Resonance Solutions of Strongly Nonlinear Systems

  • Received Date: 1999-09-17
  • Rev Recd Date: 2000-04-15
  • Publish Date: 2000-10-15
  • A new parameter transformation α=α(ε,nω0/m,ω1) was defined for extending the applicable range of the modified Lindstedt-Poincar method. It is suitable for determining subharmonic and ultraharmonic resonance solutions of strongly nonlinear systems. The 1/3 subharmonic and 3 ultraharmonic resonance solutions of the Duffing equation and the 1/2 subharmonic resonance solution of the Vander Pol-Mathieu equation were studied. These examples show approximate solutions are in good agreement with numerical solutions.
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  • [1]
    徐兆.非线性力学中一种新的渐近方法[J].力学学 报,1985,17(3):266-271.
    [2]
    Cheung Y K,Chen S H,Lau S L.A modified Lindstedt-Poincaré meth od for certain strongly nonlinear oscillators[J].Int J Non-Linear Mechanic s,1991,26(3,4):367-378.
    [3]
    李骊.强非线性系统的频闪法[J].力学学报,1990,22(4):402-412.
    [4]
    Jones S E.Remarks on the perturbation process for certain conservative systems[J].Int J Non~Linear Mechanics,1978,13(1):125-136.
    [5]
    Chen S H,Cheung Y K.A modified Lindstedt-Poincaré method for a strongly non-linear two degree of freedom system[J].Journal of Sound and Vibration,1996,193(4):751-762.
    [6]
    Chen S H,Cheung Y K.A modified Lindstedt-Poincaré method for a strongly nonlinear system with quadratic and cubic nonlinearities[J].Shock and Vibration,1996,3(4):279-285.
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