| 分数阶Duffng振子的超谐共振 |
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| 引用本文： | 申永军,杨绍普,邢海军.分数阶Duffng振子的超谐共振[J].力学学报,2012,44(4):762-768. |
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| 作者姓名： | 申永军 杨绍普 邢海军 |
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| 作者单位： | 石家庄铁道大学机械工程学院, 石家庄 050043 |
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| 基金项目： | 国家自然科学基金，河北省杰出青年科学基金，教育部新世纪优秀人才和教育部创新团队发展计划 |
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| 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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| 关 键 词： | 分数阶微分 Duffng振子 超谐共振 平均法 |
| 收稿时间： | 2011-12-20 |
| 修稿时间： | 2012-03-01 |
SUPER-HARMONIC RESONANCE OF FRACTIONAL-ORDER DUFFING OSCILLATOR |
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| Shen Yongjun,Yang Shaopu Xing Haijun.SUPER-HARMONIC RESONANCE OF FRACTIONAL-ORDER DUFFING OSCILLATOR[J].chinese journal of theoretical and applied mechanics,2012,44(4):762-768. |
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| Authors: | Shen Yongjun Yang Shaopu Xing Haijun |
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| Institution: | Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China |
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| Abstract: | The super-harmonic resonance of Duffng oscillator with fractional-order derivative is studied,and the first-order approximate solution is obtained by averaging method.The definitions of equivalent linear damping coeffcient and equivalent linear stiffness for super-harmonic resonance are established,and the effects of the fractional-order parameters on the equivalent linear damping coeffcient 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 Duffng 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. |
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| Keywords: | fractional-order derivative Duffing oscillator super-harmonic resonance averaging method |
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