分数阶Duffing振子的超谐共振

申永军; 杨绍普; 邢海军

doi:10.6052/0459-1879-11-378

分数阶Duffing振子的超谐共振

doi: 10.6052/0459-1879-11-378

石家庄铁道大学机械工程学院, 石家庄 050043

基金项目: 国家自然科学基金(11072158,10932006);河北省杰出青年科学基金(E2010002047);教育部新世纪优秀人才和教育部创新团队发展计划(IRT0971)资助项目.

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中图分类号: O313;O322
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出版历程
- 收稿日期: 2011-12-20
- 修回日期: 2012-03-01
- 刊出日期: 2012-07-18

SUPER-HARMONIC RESONANCE OF FRACTIONAL-ORDER DUFFING OSCILLATOR

Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

Funds: The project was supported by the National Natural Science Foundation of China (11072158, 10932006); Natural Science Funds for Distinguished Young Scholar of Hebei Province (E2010002047); the Program for New Century Excellent Talents in University and the Program for Changjiang Scholars and Innovative Research Team in University (IRT0971).

摘要

摘要: 研究了含分数阶微分项的Duffing振子的超谐共振,通过平均法得到了系统的一阶近似解. 提出了超谐共振时等效线性阻尼和等效线性刚度的概念,分析了分数阶微分项的系数和阶次对等效线性阻尼和等效线性刚度的影响. 建立了超谐共振解的幅频曲线的解析表达式和稳定性判断准则,对分数阶Duffing振子与传统整数阶Duffing振子的超谐共振解进行了比较. 最后通过数值仿真研究了分数阶微分项的参数对超谐共振幅频曲线的影响.
- 分数阶微分 /
- Duffing振子 /
- 超谐共振 /
- 平均法
Abstract: The super-harmonic resonance of Duffing oscillator with fractional-order derivative is studied, and the first-order approximate solution is obtained by averaging method. The definitions of equivalent linear damping coefficient and equivalent linear stiffness for super-harmonic resonance are established, and the effects of the fractional-order parameters on the equivalent linear damping coefficient and equivalent linear stiffness are also analyzed. The amplitude-frequency equation for steady-state solution associated with the stability condition is also presented, and the comparisons of the fractional-order and the traditional integer-order Duffing oscillator are fulfilled. At last the numerical simulation is used to analyze the effects of the parameters in fractional-order derivative on the amplitude-frequency curves.
- fractional-order /
- derivative /
- Duffing /
- oscillator

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参考文献(17)

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