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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September 2016
Research-Article
Subharmonic Resonance of Duffing Oscillator With Fractional-Order Derivative
Nguyen Van Khang,
Nguyen Van Khang
Department of Applied Mechanics,
Hanoi University of Science and Technology,
Hanoi 100000, Vietnam
e-mail: khang.nguyenvan2@hust.edu.vn
Hanoi University of Science and Technology,
Hanoi 100000, Vietnam
e-mail: khang.nguyenvan2@hust.edu.vn
Search for other works by this author on:
Truong Quoc Chien
Truong Quoc Chien
Department of Applied Mechanics,
Hanoi University of Science and Technology,
Hanoi 100000, Vietnam
e-mail: chienams@gmail.com
Hanoi University of Science and Technology,
Hanoi 100000, Vietnam
e-mail: chienams@gmail.com
Search for other works by this author on:
Nguyen Van Khang
Department of Applied Mechanics,
Hanoi University of Science and Technology,
Hanoi 100000, Vietnam
e-mail: khang.nguyenvan2@hust.edu.vn
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
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. Sep 2016, 11(5): 051018 (8 pages)
Published Online: May 12, 2016
Article history
Received:
August 21, 2015
Revised:
February 19, 2016
Citation
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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