| 一类强非线性系统共振周期解的渐近分析 |
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| 引用本文： | 彭献,陈自力.一类强非线性系统共振周期解的渐近分析[J].动力学与控制学报,2004,2(1):46-50. |
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| 作者姓名： | 彭献 陈自力 |
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| 作者单位： | 1. 湖南大学工程力学系,长沙,410082
2. 湖南大学工程力学系,长沙,410082;中南林学院建筑工程学院,株洲,412006 |
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| 基金项目： | 湖南省自然科学基金资助项目(01JJY2007)．~~ |
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| 摘 要： | 强非线性系统经引入参数变换，并在一定的假设条件下，可转化为弱非线性系统．将其解展成为改进的傅立叶级数后，利用参数待定法可方便地求出强非线性系统的共振周期解．研究了Duffing方程的主共振、Van der Pol方程的3次超谐共振和Van der Pol-Mathieu方程的1／2亚谐共振周期解．这些例子表明近似解与数值解非常吻合。
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| 关 键 词： | 非线性系统 共振 参数变换 傅立叶级数 渐近法 |
| 收稿时间： | 2/6/2004 12:00:00 AM |
| 修稿时间： | 2004年2月6日 |
Asymptotic analysis for resonance cycle solution of a type of strongly nonlinear systems |
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| Peng Xian and Chen Zili.Asymptotic analysis for resonance cycle solution of a type of strongly nonlinear systems[J].Journal of Dynamics and Control,2004,2(1):46-50. |
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| Authors: | Peng Xian and Chen Zili |
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| Abstract: | Based on a certain hypothesis, the strongly nonlinear system was transformed into a weakly nonlinear system by introducing a parameter transformation. Its solutions were expanded into the improved Fourier series. and the resonance cycle solutions were conveniently obtained by the undetermined parameter method. Using the method, we studied the principal resonance cycle solutions of the Duffing equation, the 3 ultraharmonic resonance cycle solutions of the Van der Pol equation, and the 1/2 subharmonic resonance cycle solutions of the Van der Pol-Mathieu equation. The examples showed that the approximate solutions closely coincided with numerical solutions. |
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| Keywords: | nonlinear system resonance parameter transformation improved Fourier series |
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