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Research Papers

Subharmonic Resonance of Duffing Oscillator With Fractional-Order Derivative

[+] Author and Article Information
Nguyen Van Khang

Department of Applied Mechanics,
Hanoi University of Science and Technology,
Hanoi 100000, Vietnam
e-mail: khang.nguyenvan2@hust.edu.vn

Truong Quoc Chien

Department of Applied Mechanics,
Hanoi University of Science and Technology,
Hanoi 100000, Vietnam
e-mail: chienams@gmail.com

1Corresponding author.

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.

J. Comput. Nonlinear Dynam 11(5), 051018 (May 12, 2016) (8 pages) Paper No: CND-15-1251; doi: 10.1115/1.4032854 History: Received August 21, 2015; Revised February 19, 2016

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.

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References

Figures

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Fig. 1

Effects of the fractional-order parameters on the existence condition for the 1/3 subharmonic resonance: p = 0.25, cp is changed

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Fig. 2

Effects of the fractional-order parameters on the existence condition for the 1/3 subharmonic resonance: cp = 0.01, p is changed

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Fig. 4

Effects of the fractional order p

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Fig. 5

Effects of the fractional coefficient cp

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Fig. 6

Effects of the coefficient E0 on the amplitude–frequency curve

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Fig. 3

The amplitude–frequency curve

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