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分数阶Duffing振子的超谐共振

申永军 杨绍普 邢海军

申永军, 杨绍普, 邢海军. 分数阶Duffing振子的超谐共振[J]. 力学学报, 2012, (4): 762-768. doi: 10.6052/0459-1879-11-378
引用本文: 申永军, 杨绍普, 邢海军. 分数阶Duffing振子的超谐共振[J]. 力学学报, 2012, (4): 762-768. doi: 10.6052/0459-1879-11-378
Shen Yongjun, Yang Shaopu, Xing Haijun. SUPER-HARMONIC RESONANCE OF FRACTIONAL-ORDER DUFFING OSCILLATOR[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, (4): 762-768. doi: 10.6052/0459-1879-11-378
Citation: Shen Yongjun, Yang Shaopu, Xing Haijun. SUPER-HARMONIC RESONANCE OF FRACTIONAL-ORDER DUFFING OSCILLATOR[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, (4): 762-768. 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
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.
详细信息
  • 中图分类号: O313;O322

SUPER-HARMONIC RESONANCE OF FRACTIONAL-ORDER DUFFING OSCILLATOR

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: 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.

     

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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

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