| 多频激励作用下Duffing-van der Pol系统的分岔 |
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| 引用本文： | 董建宁,申永军,杨绍普.多频激励作用下Duffing-van der Pol系统的分岔[J].石家庄铁道学院学报,2006,19(1):62-66. |
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| 作者姓名： | 董建宁 申永军 杨绍普 |
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| 作者单位： | 石家庄铁道学院机械工程分院 河北石家庄050043 |
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| 摘 要： | 首先利用多尺度法分析了Duffing-van der Pol系统在多频激励下的主共振响应,得到了该系统的一次近似解。然后利用数值方法研究了系统参数对近似解幅频曲线的影响。最后,运用奇异性理论得到了系统的全部分岔响应曲线,为这一类系统的动态分析与设计提供了理论依据。
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| 关 键 词： | 多频激励 Duffing系统 vanderPol系统 分岔 奇异性理论 |
| 文章编号： | 1006-3226(2006)01-0062-05 |
| 修稿时间： | 2004年10月15 |
Main Resonance of Duffing- van der Pol System to Multi - Frequency Excitations |
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| Dong Jianning,Shen Yongjun,Yang Shaopu.Main Resonance of Duffing- van der Pol System to Multi - Frequency Excitations[J].Journal of Shijiazhuang Railway Institute,2006,19(1):62-66. |
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| Authors: | Dong Jianning Shen Yongjun Yang Shaopu |
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| Abstract: | In this paper,the main resonance of nonlinear Duffing-van der Pol system to multi-frequency excitations is investigated,and the MultiScale Method is used to obtain the first-order approximate solution.Then the effects of system parameters on the frequency-amplitude curve are studied by means of numerical technology.Finally,all the bifurcation curves are obtained using the singularity theory,which provides theoretical basis for dynamic analysis and design of this kind of systems. |
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| Keywords: | multi-frequency excitation Duffing system van der Pol system bifurcation singularity theory |
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