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Research Papers

Resonance Analysis of Fractional-Order Mathieu Oscillator

[+] Author and Article Information
Jiangchuan Niu

School of Mechanical Engineering,
Shijiazhuang Tiedao University,
Shijiazhuang 050043, China
e-mail: menjc@163.com

Hector Gutierrez

Department of Mechanical
& Aerospace Engineering,
Florida Institute of Technology,
Melbourne, FL 32901
e-mail: hgutier@fit.edu

Bin Ren

School of Mechanical Engineering,
Shijiazhuang Tiedao University,
Shijiazhuang 050043, China
e-mail: renbin@stdu.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 20, 2017; final manuscript received March 1, 2018; published online March 23, 2018. Assoc. Editor: Zaihua Wang.

J. Comput. Nonlinear Dynam 13(5), 051003 (Mar 23, 2018) (8 pages) Paper No: CND-17-1511; doi: 10.1115/1.4039580 History: Received November 20, 2017; Revised March 01, 2018

The resonant behavior of fractional-order Mathieu oscillator subjected to external harmonic excitation is investigated. Based on the harmonic balance (HB) method, the first-order approximate analytical solutions for primary resonance and parametric-forced joint resonance are obtained, and the higher-order approximate steady-state solution for parametric-forced joint resonance is also obtained, where the unified forms of the fractional-order term with fractional order between 0 and 2 are achieved. The correctness of the approximate analytical results is verified by numerical results. The effects of the fractional order and parametric excitation frequency on the resonance response of the system are analyzed in detail. The results show that the HB method is effective to analyze dynamic response in a fractional-order Mathieu system.

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Copyright © 2018 by ASME
Topics: Resonance , Excitation
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Figures

Grahic Jump Location
Fig. 13

First peak value of parametric-forced joint resonance with Ω

Grahic Jump Location
Fig. 1

Comparison of primary resonance for p = 0.5

Grahic Jump Location
Fig. 2

Comparison of primary resonance for p = 1

Grahic Jump Location
Fig. 3

Comparison of primary resonance for p = 1.5

Grahic Jump Location
Fig. 4

Verification of first-order approximation for Ω = 0.05 and p = 0.5

Grahic Jump Location
Fig. 5

Verification of first-order approximation for Ω = 0.05 and p = 1

Grahic Jump Location
Fig. 6

Verification of first-order approximation for Ω = 0.05 and p = 1.5

Grahic Jump Location
Fig. 7

Verification of higher-order approximation for Ω = 0.5 and p = 0.5

Grahic Jump Location
Fig. 8

Verification of higher-order approximation for Ω = 0.5 and p = 1

Grahic Jump Location
Fig. 9

Verification of higher-order approximation for Ω = 0.5 and p = 1.5

Grahic Jump Location
Fig. 10

Peak amplitude value of primary resonance with p

Grahic Jump Location
Fig. 11

Frequency of the primary resonance with p

Grahic Jump Location
Fig. 12

Peak value of parametric-forced joint resonance with p

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