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| 非线性自治振动系统同宿解的广义双曲函数摄动法 | |
| 引用本文： | 陈洋洋,燕乐纬,佘锦炎,陈树辉. 非线性自治振动系统同宿解的广义双曲函数摄动法[J]. 应用数学和力学, 2012, 33(9): 1064-1077. DOI: 10.3879/j.issn.1000-0887.2012.09.004 |
| 作者姓名： | 陈洋洋 燕乐纬 佘锦炎 陈树辉 |
| 作者单位： | 广州大学, 减震控制与结构安全教育部重点实验室, 广州 510405; |
| 基金项目： | Project supported by the National Natural Science Foundation of China，the Natural Science Foundation of Guangdong Province of China，the Foundation of Guangdong Education Department of China，the Foundation of Guangzhou Education Bureau of China，the Research Grant Council of Hong Kong of China |
| 摘 要： | 提出广义的双曲函数摄动法,用于求解强非线性自治振子的同宿解,克服一般摄动步骤中派生方程须存在显式精确同宿解的限制．以广义双曲函数作为摄动步骤的基本函数,拓展了基于双曲函数的摄动法的适用范围．对同时含2,3次和含4次强非线性项的系统进行求解分析,验证了方法的有效性和精度． |
| 关 键 词： | 广义双曲函数摄动法 自激系统 同宿解 |
| 收稿时间： | 2012-05-08 |
Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems |
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| Yang-yang CHEN , Le-wei YAN , Kam-yim SZE , Shu-hui CHEN , Li-qun CHEN. Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1064-1077. DOI: 10.3879/j.issn.1000-0887.2012.09.004 | |
| Authors: | Yang-yang CHEN Le-wei YAN Kam-yim SZE Shu-hui CHEN Li-qun CHEN |
| Affiliation: | 1. Key Laboratory of Vibration Control and Structural Safety of Ministry of Education of China,Guangzhou University, Guangzhou 510405, P. R. China 2. Department of Engineering Mechanics, Guangzhou University,Guangzhou 510405, P. R. China 3. Department of Mechanical Engineering, The University of Hong Kong,Pokfulam, Hong Kong, P. R. China 4. Department of Applied Mechanics and Engineering, Sun Yat-sen University,Guangzhou 510275, P. R. China |
| Abstract: | A generalized hyperbolic perturbation method was presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation procedure was improved for those systems whose exact homoclinic generating solutions could not be explicitly derived. The generalized hyperbolic functions were employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method. Several strongly nonlinear oscillators with quadratic, cubic and quartic nonlinearity were studied in details to illustrate the efficiency and accuracy of the present method. |
| Keywords: | generalized hyperbolic perturbation method nonlinear autonomous system homoclinic solution |
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