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Study on chaos of nonlinear suspension system with fractional-order derivative under random excitation

Author

Listed:
  • Chen, Enli
  • Xing, Wuce
  • Wang, Meiqi
  • Ma, Wenli
  • Chang, Yujian

Abstract

The chaotic motion of a suspension system with fractional order differential under random excitation is studied. The critical condition of chaos in the mean square sense of suspension system is derived by using random Melnikov method. The function relationship between the parameters of suspension system and chaos threshold is established. The boundary curve of chaos is obtained. The influence of fractional differential parameters on chaos boundary curve is studied. The numerical simulation of fractional order suspension system is carried out, and the time domain diagram and frequency of the system are calculated the spectrum, phase plane, Poincare section and the maximum Lyapunov exponent were obtained. The results show that there is chaotic motion in the suspension system with fractional differential under random road excitation, and the coefficient and order of fractional differential term will change the boundary conditions of chaos.

Suggested Citation

  • Chen, Enli & Xing, Wuce & Wang, Meiqi & Ma, Wenli & Chang, Yujian, 2021. "Study on chaos of nonlinear suspension system with fractional-order derivative under random excitation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006548
    DOI: 10.1016/j.chaos.2021.111300
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    References listed on IDEAS

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    1. Litak, Grzegorz & Borowiec, Marek & Friswell, Michael I. & Przystupa, Wojciech, 2009. "Chaotic response of a quarter car model forced by a road profile with a stochastic component," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2448-2456.
    2. Koumene Taffo, G.I. & Siewe Siewe, M. & Tchawoua, C., 2016. "Stability switches and bifurcation in a two-degrees-of-freedom nonlinear quarter-car with small time-delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 226-239.
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    Cited by:

    1. Zhang, Yufeng & Li, Jing & Zhu, Shaotao & Ma, Zerui, 2024. "Harmonic resonance and bifurcation of fractional Rayleigh oscillator with distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 281-297.
    2. Ávalos-Ruíz, L.F. & Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Cortes-Campos, H.M. & Lavín-Delgado, J.E., 2023. "A RGB image encryption technique using chaotic maps of fractional variable-order based on DNA encoding," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. Zhou, Biliu & Jin, Yanfei & Xu, Huidong, 2022. "Global dynamics for a class of tristable system with negative stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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