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Analysis of the multistable vibration mechanism of a fractional-order quarter-car suspension under multi-frequency excitation

Author

Listed:
  • Ren, Jiani
  • Xie, Jiaquan
  • Shi, Wei
  • Wang, Zhonghua
  • Liang, Jianguo

Abstract

This paper explores the multi-steady-state vibration mechanism of a fractional-order quarter-car suspension under multi-frequency excitation. First, the multiscale method is used to derive an approximate analytical solution for multi-steady-state vibration, and stability criteria for steady-state responses are established by combining the Hartman-Grobman theorem and Routh-Hurwitz criterion. The method's accuracy is verified by comparing the analytical solution with the attraction domain from cell mapping numerical simulation. Analysis shows the system has notable multi-steady-state features in a specific frequency coupling interval; its stable and unstable solutions undergo bifurcation evolution with frequency ratio changes. Stiffness-hardening suspensions can exhibit bistable, tristable, or quadri-stable periodic vibrations, while stiffness-softening ones, though having four steady-state periodic vibration modes, show dynamic responses with unbounded regions and fractal characteristics. Finally, the regulation mechanism of fractional-order parameters on saddle-node (SN) bifurcation characteristics is investigated, and the intrinsic relationship between parameter variations and the evolution of the number of solution branches is clarified. Results indicate reasonable adjustments of fractional-order damping parameters can effectively control the stable support range and attraction domain distribution, providing theoretical support for revealing the multi-steady-state vibration mechanism of fractional-order suspensions and engineering references for optimizing suspension dynamic performance.

Suggested Citation

  • Ren, Jiani & Xie, Jiaquan & Shi, Wei & Wang, Zhonghua & Liang, Jianguo, 2026. "Analysis of the multistable vibration mechanism of a fractional-order quarter-car suspension under multi-frequency excitation," Chaos, Solitons & Fractals, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:chsofr:v:206:y:2026:i:c:s0960077925018673
    DOI: 10.1016/j.chaos.2025.117853
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