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Chaotic response of a quarter car model forced by a road profile with a stochastic component

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  • Litak, Grzegorz
  • Borowiec, Marek
  • Friswell, Michael I.
  • Przystupa, Wojciech

Abstract

The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos in the case of a quarter car model excited kinematically by a road surface profile consisting of harmonic and noisy components. By analyzing the potential an analytic expression is found for the homoclinic orbit. The road profile excitation including harmonic and random characteristics as well as the damping are treated as perturbations of a Hamiltonian system. The critical Melnikov amplitude of the road surface profile is found, above which the system can vibrate chaotically. This transition is analyzed for different levels of noise and illustrated by numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2448-2456
    DOI: 10.1016/j.chaos.2007.07.021
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    References listed on IDEAS

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    1. Litak, G. & Borowiec, M. & Ali, M. & Saha, L.M. & Friswell, M.I., 2007. "Pulsive feedback control of a quarter car model forced by a road profile," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1672-1676.
    2. Gan, Chunbiao, 2005. "Noise-induced chaos and basin erosion in softening Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1069-1081.
    3. Huang, Dong-Wei & Gao, Qin & Wang, Hong-Li & Feng, Jian-Feng & Zhu, Zhi-Wen, 2007. "On chaotic motion of some stochastic nonlinear dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 242-246.
    4. Yang, Xiaoli & Xu, Wei & Sun, Zhongkui, 2006. "Effect of bounded noise on the chaotic motion of a Duffing Van der pol oscillator in a ϕ6 potential," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 778-788.
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    1. 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).

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