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Research Papers

On the Weak Signal Amplification by Twice Sampling Vibrational Resonance Method in Fractional Duffing Oscillators

[+] Author and Article Information
Jin-Rong Yang, Cheng-Jin Wu, Hou-Guang Liu

School of Mechatronic Engineering,
China University of Mining and Technology,
Xuzhou 221116, China

Jian-Hua Yang

School of Mechatronic Engineering,
China University of Mining and Technology,
Xuzhou 221116, China;
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109;
Jiangsu Key Laboratory of Mine
Mechanical and Electrical Equipment,
China University of Mining and Technology,
Xuzhou 221116, China
e-mail: jianhuayang@cumt.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 20, 2017; final manuscript received December 10, 2017; published online January 24, 2018. Assoc. Editor: Dumitru Baleanu.

J. Comput. Nonlinear Dynam 13(3), 031009 (Jan 24, 2018) (7 pages) Paper No: CND-17-1427; doi: 10.1115/1.4038778 History: Received September 20, 2017; Revised December 10, 2017

In our former work developed by Yang et al. (2017, “Enhancing the Weak Signal With Arbitrary High-Frequency by Vibrational Resonance in Fractional-Order Duffing Oscillators,” ASME J. Comput. Nonlinear Dyn., 12(5), p. 051011), we put forward the rescaled vibrational resonance (VR) method in fractional duffing oscillators to amplify a weak signal with arbitrary high frequency. In the present work, we propose another method named as twice sampling VR to achieve the same goal. Although physical processes of two discussed methods are different, the results obtained by them are identical completely. Besides the two external signals excitation case, the validity of the new proposed method is also verified in the system that is excited by an amplitude modulated signal. Further, the dynamics of the system reveals that the resonance performance, i.e., the strength and the pattern, depends on the fractional order closely.

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Figures

Grahic Jump Location
Fig. 1

The response amplitude versus the strength of the auxiliary signal under different fractional-order values. The simulation parameters are ω = 1500, f = 0.1, κ = 40, β = γ = 6000, a1 = –1, b1 = 1, a = −1, and b = 1. Line 1 and line 2 are the results obtained by the rescaled VR method and the twice sampling VR method, respectively.

Grahic Jump Location
Fig. 2

The optimal VR output under different values of the fractional order. The simulation parameters are ω = 1500, f = 0.1, κ = 40, β = γ = 6000, a1 = −1, b1 = 1, a = −1 and b = 1. Subplots (a), (c), and (e) are obtained by the rescaled VR method. Subplots (b), (d), and (f) are obtained by the twice sampling VR method.

Grahic Jump Location
Fig. 3

The response amplitude versus the strength of the auxiliary signal under different fractional-order and character signal frequency values. In (a), (c) and (e), ω = 200 and β = γ = 800; in (b), (d) and (f), ω = 2000 and β = γ = 8000. Other simulation parameters are f = 0.01, κ = 40, a1 = −1, b1 = 1, a = −1 and b = 1. Lines 1 and 2 are the results obtained by the rescaled VR method and the twice sampling VR method, respectively.

Grahic Jump Location
Fig. 4

The response amplitude versus the strength of the auxiliary signal under different fractional-order values. The simulation parameters are f = 0.01, ω = 1500, κ = 40, β = γ = 7500, δ = 1.2, a1 = −1, b1 = 1, a = –1, and b = 1. Line 1 and line 2 are the results obtained by the rescaled VR method and the twice sampling VR method, respectively.

Grahic Jump Location
Fig. 5

The response amplitude versus the strength of the auxiliary signal under different fractional order and character signal frequency values. In (a), (c) and (e), ω = 200 and β = γ = 1000; in (b), (d) and (f), ω = 2000 and β = γ = 10,000. Other simulation parameters are f = 0.01, κ = 40, δ = 1.0, a1 = −1, b1 = 1, a = −1 and b = 1. Lines 1 and 2 are the results obtained by the rescaled VR method and the twice sampling VR method, respectively.

Grahic Jump Location
Fig. 6

The response amplitude versus the strength of the auxiliary signal under different fractional-order values. The simulation parameters are ω = 1500, f = 0.1, κ = 40, β = γ = 6000, a1 = −1, b1 = 1, a = −1 and b = 1. Lines 1 and 2 are the results obtained by the rescaled VR method and the twice sampling VR method, respectively.

Grahic Jump Location
Fig. 7

The optimal VR output under different values of the fractional order. The simulation parameters are ω = 1500, f = 0.1, κ = 40, β = γ = 6000, a1 = −1, b1 = 1, a = −1 and b = 1. Subplots (a), (c), (e) are obtained by the rescaled VR method. Subplots (b), (d), and (f) are obtained by the twice sampling VR method.

Grahic Jump Location
Fig. 8

The response amplitude versus the strength of the auxiliary signal under different fractional order and character signal frequency values. In (a), (c) and (e), ω = 200 and β = γ = 1000; in (b), (d) and (f), ω = 2000 and β = γ = 10,000. Other simulation parameters are f = 0.01, κ = 40, a1 = −1, b1 = 1, a = −1 and b = 1. Lines 1 and 2 are the results obtained by the rescaled VR method and the twice sampling VR method, respectively.

Grahic Jump Location
Fig. 9

The response amplitude versus the strength of the auxiliary signal under different fractional-order values. The simulation parameters are ω = 1500, f = 0.005, κ = 40, β = γ = 7500, δ = 1.2, a1 = −1, b1 = 1, a = −1 and b = 1. Lines 1 and 2 are the results obtained by the rescaled VR method and the twice sampling VR method, respectively.

Grahic Jump Location
Fig. 10

The response amplitude versus the strength of the auxiliary signal under different fractional-order and character signal frequency values. In (a), (c) and (e), ω = 200 and β = γ = 1000; in (b), (d) and (f), ω = 2000 and β = γ = 10,000. Other simulation parameters are f = 0.01, κ = 40, δ = 1.2, a1 = −1, b1 = 1, a = −1 and b = 1. Lines 1 and 2 are the results obtained by the rescaled VR method and the twice sampling VR method, respectively.

Grahic Jump Location
Fig. 11

Flowcharts of the two VR methods when the theory will be realized by the experimental hardware devices

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