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一类含五次非线性恢复力的Duffing系统共振与分岔特性分析

彭荣荣

彭荣荣. 一类含五次非线性恢复力的Duffing系统共振与分岔特性分析[J]. 应用数学和力学, 2019, 40(10): 1122-1134. doi: 10.21656/1000-0887.390234
引用本文: 彭荣荣. 一类含五次非线性恢复力的Duffing系统共振与分岔特性分析[J]. 应用数学和力学, 2019, 40(10): 1122-1134. doi: 10.21656/1000-0887.390234
PENG Rongrong. Analysis of Resonance and Bifurcation Characteristics of Some Duffing Systems With Quintic Nonlinear Restoring Forces[J]. Applied Mathematics and Mechanics, 2019, 40(10): 1122-1134. doi: 10.21656/1000-0887.390234
Citation: PENG Rongrong. Analysis of Resonance and Bifurcation Characteristics of Some Duffing Systems With Quintic Nonlinear Restoring Forces[J]. Applied Mathematics and Mechanics, 2019, 40(10): 1122-1134. doi: 10.21656/1000-0887.390234

一类含五次非线性恢复力的Duffing系统共振与分岔特性分析

doi: 10.21656/1000-0887.390234
基金项目: 2018年度江西省教育厅科学技术研究资助项目(GJJ181061)
详细信息
    作者简介:

    彭荣荣(1987—),男,讲师,硕士(E-mail: 15294476178@163.com).

  • 中图分类号: O322;O411.3

Analysis of Resonance and Bifurcation Characteristics of Some Duffing Systems With Quintic Nonlinear Restoring Forces

  • 摘要: 考虑一类含有外激力和五次非线性恢复力的Duffing系统,运用多尺度法求解得到该系统的幅频响应方程,给出不同参数变化下的幅频特性曲线及变化规律,同时利用奇异性理论得到该系统在3种情形下的转迁集及对应的拓扑结构.其次确定系统的不动点,运用Hamilton函数给出该系统的异宿轨,在此基础上,利用Melnikov方法得到该系统在Smale马蹄意义下发生混沌的阈值.而后通过数值仿真给出了系统随外激力、五次非线性项系数变化下的动态分岔与混沌行为,发现存在周期运动、倍周期运动、拟周期运动及混沌等非线性现象.最后运用Lyapunov指数、相轨图和Poincaré截面等非线性方法对理论的正确性进行验证.上述研究结论为进一步提升对Duffing系统非线性特性及其演化规律的认识提供了一定的理论参考.
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出版历程
  • 收稿日期:  2018-09-04
  • 修回日期:  2018-11-28
  • 刊出日期:  2019-10-01

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