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

TANG Jia-shi

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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.

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.

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

TANG Jia-shi

Department of Engineering Mechanics, Hunan University, Changsha 410082, P. R. China

Received Date: 1999-09-17
Rev Recd Date: 2000-04-15
Publish Date: 2000-10-15

Abstract

Abstract

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.
- strongly nonlinear system,
- subharmonic and ultraharmonic resonance,
- parameter transformation

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References(6)

References

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