分数阶阻尼Duffing系统的非线性动力学特性研究

曹军义; 谢航; 蒋庄德

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分数阶阻尼Duffing系统的非线性动力学特性研究

专题研究 | 更新时间：2025-07-09

- 分数阶阻尼Duffing系统的非线性动力学特性研究
- Nonlinear Dynamics of Duffing System with Fractional Order Damping
- 西安交通大学学报 2009年43卷第3期页码：50-54
- 作者机构：
  
  西安交通大学机械制造系统工程国家重点实验室,西安,710049
- 作者简介：
- 基金信息：
  
  : 2008-05-16. 作者简介: 曹军义(1977-),男,博士,讲师. 基金项目: 国家自然科学基金资助项目(50805113,50775175);中国博士后科学基金资助项目(20080441173)
- DOI：
  中图分类号： TP273
- 网络首发：2009-03-10，
  
  纸质出版：2009
- 稿件说明：
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曹军义, 谢航, 蒋庄德. 分数阶阻尼Duffing系统的非线性动力学特性研究[J]. 西安交通大学学报, 2009,43(3):50-54.

Nonlinear Dynamics of Duffing System with Fractional Order Damping[J]. 2009, 43(3): 50-54.
曹军义, 谢航, 蒋庄德. 分数阶阻尼Duffing系统的非线性动力学特性研究[J]. 西安交通大学学报, 2009,43(3):50-54. DOI：

Nonlinear Dynamics of Duffing System with Fractional Order Damping[J]. 2009, 43(3): 50-54. DOI：

摘要

采用4阶龙格库塔法和10阶连分式欧拉法

数值计算、分析了分数阶阻尼Duffing系统的动力学特性.利用相图、Poincare截面映射图和分岔图等非线性动力学分析方法研究了阻尼的分数阶微积分阶数对Duffing系统动力学性能的影响

采用分岔图法研究了外部激励的幅值和频率变化时分数阶阻尼Duffing系统的动力学行为.分析表明

分数阶阻尼的阶数在0.1～2.0发生变化时

系统依次进入周期运动、混沌运动、周期运动、混沌运动和周期运动

并且在混沌运动区间中存在着周期运动窗口

由周期运动进入混沌运动的倍周期过程比较明显

结果证实了阻尼的分数阶微分阶数对系统的动力学特性影响比较大

因此在系统动力学设计和分析中应该重视.

Abstract

Nonlinear dynamics of Duffing system with fractional order damping is investigated. The equations of fractional order damped Duffing system are established. The four-order Runge-Kutta method and ten-order CFE-Euler methods are performed to solve the fractional order Duffing equations. The effects of fractional order on the system dynamics are proposed with phase diagrams

bifurcation diagrams and Poincare map. The bifurcation diagram is utilized to analyze the effect of excitation amplitude and frequency on Duffing system with fractional order damping. The analysis shows that the fractional order damped Duffing system exhibits period motion

chaos

period motion

chaos

period motion one by one when the fractional order change from 0.1 to 2.0. A period doubling route to chaos is appeared clearly. The numerical results verify the significant effect of fractional order on system dynamics. It is necessary to consider the fractional order of damping in the design and analysis of system dynamics.

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references

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