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Resonance and attraction domain analysis of asymmetric duffing systems with fractional damping in two degrees of freedom

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  • Xie, Jiaquan
  • Xie, Zhikuan
  • Xu, Huidong
  • Li, Zhanlong
  • Shi, Wei
  • Ren, Jiani
  • Shi, Haoming

Abstract

This article establishes a two degree of freedom asymmetric Duffing system model with fractional damping through the study of the Jeffcott rotor system with horizontal support, and analyzes the dynamic behavior of its resonance and attraction domain structures. The second-order approximate solution of the system equation is obtained using a multiscale method, and the slow flow modulation equations of both the amplitudes and phases are extracted. The comparison between approximate and numerical solutions has shown their high consistency and the Routh Hurwitz criterion is utilized to study the stability of the system. Finally, we explore the effect of fractional damping on the vibration behavior of the system using amplitude frequency curves, attractive watersheds, and time trajectory plots, including both negative and positive values of the nonlinear stiffness coefficient. The analysis shows that if the coefficient and order of the fractional damping term are reasonably selected, the horizontal and vertical displacements of the system vibration can be effectively controlled. The importance of this work lies in its application in rotor vibration, which has significant implications for the study of the system under investigation.

Suggested Citation

  • Xie, Jiaquan & Xie, Zhikuan & Xu, Huidong & Li, Zhanlong & Shi, Wei & Ren, Jiani & Shi, Haoming, 2024. "Resonance and attraction domain analysis of asymmetric duffing systems with fractional damping in two degrees of freedom," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009925
    DOI: 10.1016/j.chaos.2024.115440
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    References listed on IDEAS

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    1. Cai, Chengcai & Shen, Yongjun & Wen, Shaofang, 2023. "Simultaneously primary and super-harmonic resonance of a van der Pol oscillator with fractional-order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Cui, Diandian & Shang, Huilin, 2024. "Global dynamic analysis of a typical tristable piezoelectric energy harvester for performance enhancement," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    3. Wen, Shao-Fang & Shen, Yong-Jun & Yang, Shao-Pu & Wang, Jun, 2017. "Dynamical response of Mathieu–Duffing oscillator with fractional-order delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 54-62.
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