Freedom in multiple-scale analysis of undamped free harmonic oscillators with nonlinear perturbations

被引：0

作者：

Elkhoga, Salwa M. ^{[1
]}

机构：

[1] Dept. of Eng. Mathematics and Phys., Faculty of Eng., Alexandria University, Alexandria 21544, Egypt

来源：

AEJ - Alexandria Engineering Journal | 2001年 / 40卷 / 06期

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摘要：

In this work, some choices of the free amplitudes that result in the solution of the undamped free anharmonic oscillator (Duffing's equation) obtained by the Method of Multiple Scales (MMS) are investigated. The equations that represent the solvability condition of each order of the solution up to third order are derived. From the successive analysis of the solvability conditions, the free amplitudes of each order are found to have the same dependence on the time scales as the fundamental one. Also the free amplitudes of each order of the solution are found to act the same role of the free resonant functions introduced in each order when the Normal Form Method (NFM) is used. The solutions resulting from some choices of the free amplitudes and their counterparts when the NFM is used are presented. Concluding remarks concerning the two methods are given.

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页码：929 / 934