非线性振动中两变量型尺度法存在的问题与改进
Defect and Improvement of Two-Time Expansion Method in Nonlinear Oscillations
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摘要: 本文指出了非线性振动中两变量型尺度法存在的问题并进行了改进.最后证明了改进的两变量型尺度法与КВМ法等价.Abstract: In this paper,the defect of the Two-Time Expansion method is indicated and an improvement of this method is suggested.Certain examples.in which the present method is used,are given.Moreover,the paper shows the equivalence of the improved Two-Time Expansion Method and the method of КВМ(Крылов-Воголюбов-Мигроцолъский)
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[1] 包戈留包夫,Н.Н.Ю.А.米特罗波尔斯基,《非线性振动理论中的渐近方法》,金福监等译,上海科学出版社(1963). [2] Mickens,Ronald Elbert,An Introduction to Nonlinear Oscillation,Cambridge University Press,Cambridge(1981). [3] Nayfeh,A.H.and D.T.Mook,Nonlinear Oscillations,Wiley,New York(1979). [4] 吴福光,蔡承武、徐兆,《振动理论》,下册,中山大学(1983). [5] 郑兆昌主编,《机械振动》,机械工业出版社(1986). [6] 江福汝,奇异摄动理论概述,《奇异摄动理论及其在力学中的应用》(钱伟长主编),科学出版社(1981). [7] Cole,J.D.and J.Kevorkian,Uniformly valid asymptotic approximations for certain nonlinear differential equations,Nonlinear Differential Equations and Nonlinear Mechanics,ed.by P.Joseph,La Salle and Solomon Lefschetz,Academic Press Inc.,New York(1963),113-120.
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