THE MLP METHOD FOR SUBHARMONIC AND ULTRA-HARMONIC RESONANCE SOLUTIONS OF STRONGLY NONLINEAR SYSTEMS

Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (10): 1153-1160.

THE MLP METHOD FOR SUBHARMONIC AND ULTRA-HARMONIC RESONANCE SOLUTIONS OF STRONGLY NONLINEAR SYSTEMS

唐驾时

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

收稿日期:1999-09-17 修回日期:2000-04-15 出版日期:2000-10-18 发布日期:2000-10-18

THE MLP METHOD FOR SUBHARMONIC AND ULTRA-HARMONIC RESONANCE SOLUTIONS OF STRONGLY NONLINEAR SYSTEMS

TANG Jia-shi

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

Received:1999-09-17 Revised:2000-04-15 Online:2000-10-18 Published:2000-10-18

摘要/Abstract

摘要： A new parameter transformation α=α(ε, nω₀/m, ω₁) was defined for extending the applicable range of the modified Lindstedt-Poincaré 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 Van der Pol-Mathieu equation were studied. These examples show approximate solutions are in good agreement with numerical solutions.

中图分类号:

O322

唐驾时. THE MLP METHOD FOR SUBHARMONIC AND ULTRA-HARMONIC RESONANCE SOLUTIONS OF STRONGLY NONLINEAR SYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(10): 1153-1160.

TANG Jia-shi. THE MLP METHOD FOR SUBHARMONIC AND ULTRA-HARMONIC RESONANCE SOLUTIONS OF STRONGLY NONLINEAR SYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(10): 1153-1160.

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THE MLP METHOD FOR SUBHARMONIC AND ULTRA-HARMONIC RESONANCE SOLUTIONS OF STRONGLY NONLINEAR SYSTEMS

THE MLP METHOD FOR SUBHARMONIC AND ULTRA-HARMONIC RESONANCE SOLUTIONS OF STRONGLY NONLINEAR SYSTEMS

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