Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems

doi:10.1007/s10483-012-1611-6

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (9): 1137-1152.doi: https://doi.org/10.1007/s10483-012-1611-6

Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems

陈洋洋¹, 燕乐纬², 佘锦炎³, 陈树辉⁴

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

收稿日期:2012-05-08 修回日期:2012-05-16 出版日期:2012-09-10 发布日期:2012-09-10
通讯作者: CHEN, Professor, Ph.D., E-mail: stscsh@mail.sysu.edu.cn E-mail:stscsh@mail.sysu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 10972240 and 11102045), the Natural Science Foundation of Guangdong Province of China (No. S20110400040), the Foundation of Guangdong Education Department of China (No. LYM10108), the Foundation of Guangzhou Education Bureau of China (No. 10A024), and the Research Grant Council of Hong Kong of China (No.GRF-HKU-7173-09E)

Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems

Yang-yang CHEN¹, Le-wei YAN², Kam-yim SZE³, Shu-hui CHEN ⁴

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

Received:2012-05-08 Revised:2012-05-16 Online:2012-09-10 Published:2012-09-10
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 10972240 and 11102045), the Natural Science Foundation of Guangdong Province of China (No. S20110400040), the Foundation of Guangdong Education Department of China (No. LYM10108), the Foundation of Guangzhou Education Bureau of China (No. 10A024), and the Research Grant Council of Hong Kong of China (No.GRF-HKU-7173-09E)

摘要/Abstract

摘要：

A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation proce-dure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived. The generalized hyperbolic functions are 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 nonlin-earity are studied in detail to illustrate the efficiency and accuracy of the present method.

关键词: gas atomization, spray forming, instability of interfacial wave

Abstract:

Key words: gas atomization, spray forming, instability of interfacial wave

中图分类号:

O322

陈洋洋;燕乐纬;佘锦炎;陈树辉. Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(9): 1137-1152.

Yang-yang CHEN;Le-wei YAN;Kam-yim SZE;Shu-hui CHEN . Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(9): 1137-1152.

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Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems

Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems

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