| 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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| 应用同伦分析法研究Mathieu-Duffing振子的周期解 |
| Period solutions of Mathieu-Duffing oscillator by the homotopy analysis method |
| 投稿时间：2015-08-19 修订日期：2015-11-28 |
| DOI：10.7511/jslx201701016 |
| 中文关键词: 同伦分析法 Mathieu-Duffing振子 周期解 Floquet理论 |
| 英文关键词:the homotopy analysis method Mathieu-Duffing oscillator period motion floquet theory |
| 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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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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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