Chinese Journal of Theoretical and Applied Mechani ›› 2012, Vol. ›› Issue (4): 762-768.DOI: 10.6052/0459-1879-11-378

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SUPER-HARMONIC RESONANCE OF FRACTIONAL-ORDER DUFFING OSCILLATOR

Shen Yongjun, Yang Shaopu, Xing Haijun   

  1. Department of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
  • Received:2011-12-20 Revised:2012-03-01 Online:2012-07-23 Published:2012-07-14
  • Supported by:

    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).

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.

Key words:

fractional-order|derivative|Duffing|oscillator|super-harmonic|resonance|averaging|method

CLC Number: