| 强非线性多自由度动力系统主共振同伦分析法研究 |
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| 引用本文： | 原培新,李永强.强非线性多自由度动力系统主共振同伦分析法研究[J].应用数学和力学,2010,31(10):1229-1238. |
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| 作者姓名： | 原培新 李永强 |
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| 作者单位： | 东北大学 机械工程与自动化学院,沈阳 110004;2.东北大学 理学院,沈阳 110004 |
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| 基金项目： | 中央高校基本科研业务费专项资金资助项目 |
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| 摘 要： | 应用同伦分析方法(HAM)解决强非线性多自由度系统在谐波激振力下的主共振问题．同伦分析方法的有效性独立于所考虑的方程中是否含有的小参数．同伦分析方法提供了一个简单的方法，通过一个辅助参数h-来调节和控制级数解的收敛区域．两个具体算例表明，同伦分析方法得出的结果与修正Linstedt-Poincaré法、增量谐波平衡法的解决方案得出的结果相吻合．
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| 关 键 词： | 同伦分析法 主共振 强非线性 级数解 多自由度 |
| 收稿时间： | 1900-01-01 |
Study on Primary Resonance of Multi-Degree-of-Freedom Dynamic Systems With Strongly Non-Linearity Using the Homotopy Analysis Method |
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| YUAN Pei-xin,LI Yong-qiang.Study on Primary Resonance of Multi-Degree-of-Freedom Dynamic Systems With Strongly Non-Linearity Using the Homotopy Analysis Method[J].Applied Mathematics and Mechanics,2010,31(10):1229-1238. |
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| Authors: | YUAN Pei-xin LI Yong-qiang |
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| Institution: | Mechanical Engineering and Automation School, Northeastern University, Shenyang 110004, P. R. China; |
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| Abstract: | The homotopy analysis method (HAM) was presented for the primary resonance of multidegree-of-freedom system with strongly non-linearity excited by harmonic forces.The validity of the HAM is independent of whether or not there are small parameters in the considered equation.The HAM has provided a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter h.Two examples were presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincarémethod and the incremental harmonic balance method. |
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