In this paper, the subharmonic resonance of Duffing oscillator with fractional-order derivative is investigated using the averaging method. First, the approximately analytical solution and the amplitude–frequency equation are obtained. The existence condition for subharmonic resonance based on the approximately analytical solution is then presented, and the corresponding stability condition based on Lyapunov theory is also obtained. Finally, a comparison between the fractional-order and the traditional integer-order of Duffing oscillators is made using numerical simulation. The influences of the parameters in fractional-order derivative on the steady-state amplitude, the amplitude–frequency curves, and the system stability are also investigated.
Subharmonic Resonance of Duffing Oscillator With Fractional-Order Derivative
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 21, 2015; final manuscript received February 19, 2016; published online May 12, 2016. Assoc. Editor: Hiroshi Yabuno.
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Van Khang, N., and Chien, T. Q. (May 12, 2016). "Subharmonic Resonance of Duffing Oscillator With Fractional-Order Derivative." ASME. J. Comput. Nonlinear Dynam. September 2016; 11(5): 051018. https://doi.org/10.1115/1.4032854
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