| 应用同伦分析法研究Mathieu-Duffing振子的周期解 |
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| 引用本文： | 李云东,杨翊仁.应用同伦分析法研究Mathieu-Duffing振子的周期解[J].计算力学学报,2017,34(1):111-116. |
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| 作者姓名： | 李云东 杨翊仁 |
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| 作者单位： | 1. 四川理工学院 理学院,自贡,643000;2. 西南交通大学 力学与工程学院,成都,613001 |
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| 基金项目： | 四川省高校重点实验室开放基金（2016QZJ03）；四川理工学院校基金（2015KY02）资助项目 |
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| 摘 要： | 应用同伦分析法研究了Mathieu-Duffing振子的周期解,展示了Mathieu-Duffing振子的周期1和周期2解的求解过程,通过求解构造的非线性代数方程组而获得周期解,应用Floquet理论判别了周期解的稳定性。比较了同伦分析方法得到的周期解和数值方法得到的周期解,结果表明两者具有一致性。
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| 关 键 词： | 同伦分析法 Mathieu-Duffing振子 周期解 Floquet理论 |
| 收稿时间： | 2015/8/19 0:00:00 |
| 修稿时间： | 2015/11/28 0:00:00 |
Period solutions of Mathieu-Duffing oscillator by the homotopy analysis method |
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| LI Yun-dong,YANG Yi-ren.Period solutions of Mathieu-Duffing oscillator by the homotopy analysis method[J].Chinese Journal of Computational Mechanics,2017,34(1):111-116. |
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| Authors: | LI Yun-dong YANG Yi-ren |
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| Institution: | School of Science, Sichuan University of Science & Engineering, Zigong 643000, China;School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China |
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| Abstract: | In this paper,the period motion of the Mathieu-Duffing oscillator is investigated by the homo-topy analysis method.The procedures of the solution of the period-1 and period-2 are presented.The period solutions are obtained by solving the nonlinear algebraic equations.Stability of the period motion is judged by the Floquet theory.The phase portraits of period solution obtained by the homotopy analysis method agree well with those obtained by the numerical time-integration method. |
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| Keywords: | the homotopy analysis method Mathieu-Duffing oscillator period motion floquet theory |
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