| 类Pade逼近方法在二维非线性振动系统的应用 |
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| 引用本文： | 张琪昌,冯晶晶,王炜.类Pade逼近方法在二维非线性振动系统的应用[J].力学学报,2011,43(5):914-921. |
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| 作者姓名： | 张琪昌 冯晶晶 王炜 |
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| 作者单位： | 1.天津大学内燃机燃烧学国家重点实验室 |
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| 基金项目： | 国家自然科学基金(10872141,11072168); 国家科技重大专项(2009ZX04001-041-02); 天津大学自主创新基金资助项目~~ |
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| 摘 要： | 提出一种求解强非线性系统同异宿轨道解析解的改进类Pad\'{e}逼近方法, 该方法在分析带有扰动参数的系统时无需预先限定参数的取值范围. 首先研究了具有三次非线性项的系统,分析其产生同宿或异宿轨道时参数的取值范围, 分别提出直接体现参数的同宿及异宿解的设解通式, 据此获得了一类强非线性下的自治系统方程的同宿及异宿解. 其次, 对于非自治系统, 研究了具有三次非线性项系统的强迫振动, 直接考虑扰动参数对整个系统的影响, 得到了满足同(异)宿边界条件的周期解. 最后, 构造了两种不同形式的异宿解, 从而减少了保守系统异宿解的计算量. 借助数值模拟验证了该方法的有效性及精确性.
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| 关 键 词： | 强非线性 |
| 收稿时间： | 2011-04-01 |
| 修稿时间： | 2011-05-13 |
THE CONSTRUCTION OF HOMOCLINIC AND HETEROCLINIC ORBIT IN TWO-DIMENTSIONAL NONLINEAR SYSTEMS BASED ON THE QUASI-PADE APPROXIMATION |
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| Zhang Qichang Feng Jingjing,Wang Wei.THE CONSTRUCTION OF HOMOCLINIC AND HETEROCLINIC ORBIT IN TWO-DIMENTSIONAL NONLINEAR SYSTEMS BASED ON THE QUASI-PADE APPROXIMATION[J].chinese journal of theoretical and applied mechanics,2011,43(5):914-921. |
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| Authors: | Zhang Qichang Feng Jingjing Wang Wei |
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| Institution: | 1.State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China2.Tianjin Key Laboratory of Modern Engineering Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China |
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| Abstract: | The conventional quasi-Pade approximants are developed to study the homoclinic and heteroclinic solutions in nonlinear dynamic system,and in the solution process in which the disturbance parameters of system don't be restricted in advance.Firstly,the system with cubic nonlinear oscillators is considered.The value ranges of its parameters can be determined when the homoclinic and heteroclinic orbits are occurred.Respectively suppose the general formulations homoclinic and heteroclinic solutions which reflect... |
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| Keywords: | quasi-Pade approximations homoclinic and heteroclinic orbit global bifurcation strongly nonlinear oscillation |
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