强非线性杜芬系统的周期解及其分岔

doi:10.3969/j.issn.1000-1565.2017.05.003

河北大学学报(自然科学版) ›› 2017, Vol. 37 ›› Issue (5): 457-463.DOI: 10.3969/j.issn.1000-1565.2017.05.003

强非线性杜芬系统的周期解及其分岔

王旭,李欣业,王振静,韩善凯

收稿日期:2017-03-27 出版日期:2017-09-25 发布日期:2017-09-25
通讯作者: 李欣业(1966—),男,河北迁安人,河北工业大学教授,主要从事复杂系统的动力学建模与分析和非线性动力学与控制研究.E-mail:xylihebut@163.com
作者简介:王旭(1990—),男,河北保定人,河北工业大学在读硕士研究生. E-mail:1216380802@qq.com
基金资助:
河北省高层次人才资助项目(C201400309)

Periodic solutions and their bifurcation of Duffing system with strong non-linearity

WANG Xu, LI Xinye, WANG Zhenjing, HAN Shankai

School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China

Received:2017-03-27 Online:2017-09-25 Published:2017-09-25

摘要/Abstract

摘要： 基于广义谐波平衡法,求解了强非线性杜芬振子自由振动和简谐激励下受迫振动的周期-m解,并与数值解进行了比较,从而讨论非线性项的系数以及激励参数对系统周期解的影响.对自由振动而言,倍周期响应的周期是派生系统固有周期的整倍数;对受迫振动而言,倍周期响应的周期是外激励周期的整倍数.结果表明,为使近似解析谐波解与数值解比较接近,系统的非线性越强,所需的谐波项数越多;所设倍周期分岔解的周期越大,所需的项数也越多.

关键词: 广义谐波平衡法, 强非线性, 杜芬系统, 周期-m解

Abstract: Based on the generalized harmonic balance method, the period-m responses of free and forced Duffing oscillators are constructed and compared with numerical solutions from which the effects of nonlinear term and excitation parameters can be observed. For free vibrations, the response periods are assumed to be integer times of the natural period of the corresponding linear system and the excitation period respectively. It is shown that the number of harmonic terms should be large enough for both strongly nonlinear systems and period-doubling bifurcation solutions with large period so that the approximate analytic solutions are comparative to numerical results.

Key words: generalized harmonic balance method, strong non-linearity, Duffing systems, period-m solution

中图分类号:

O322

王旭,李欣业,王振静,韩善凯. 强非线性杜芬系统的周期解及其分岔[J]. 河北大学学报(自然科学版), 2017, 37(5): 457-463.

WANG Xu, LI Xinye, WANG Zhenjing, HAN Shankai. Periodic solutions and their bifurcation of Duffing system with strong non-linearity[J]. Journal of Hebei University (Natural Science Edition), 2017, 37(5): 457-463.

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强非线性杜芬系统的周期解及其分岔

Periodic solutions and their bifurcation of Duffing system with strong non-linearity

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