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MDoF mechanical systems with rate-independent hysteresis: Assessment of dimensionality, loop shapes, and mass ratio

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  • Capuano, Raffaele
  • Vaiana, Nicolò
  • Rosati, Luciano

Abstract

We explore the dynamic behavior of Multi Degrees of Freedom (MDoF) mechanical systems characterized by rate-independent hysteretic properties. The study focuses on three main aspects: (i) the influence of system dimensionality; (ii) the combined effect of distinct hysteretic behaviors acting on different components, and (iii) the impact of mass ratio variations on the steady-state response. To this end, a general class of nonlinear hysteretic systems is defined using a non-dimensional formulation, and a Poincaré map-based continuation procedure is employed to numerically compute periodic solutions, determine their stability, and detect bifurcations. Moreover, the adoption of the Vaiana–Rosati model of hysteresis (VRM+D) enables a unified and thorough analysis of complex hysteretic loop shapes for the first time. The results obtained in a consistent set of case studies reveal how these internal features govern resonance phenomena, affect stability, mode interactions and lead to the occurrence of advanced bifurcation patterns, including quasi-periodic oscillations and chaos.

Suggested Citation

  • Capuano, Raffaele & Vaiana, Nicolò & Rosati, Luciano, 2025. "MDoF mechanical systems with rate-independent hysteresis: Assessment of dimensionality, loop shapes, and mass ratio," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p2:s0960077925010756
    DOI: 10.1016/j.chaos.2025.117062
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    References listed on IDEAS

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    1. Lyu, Xiaohong & Zhu, Xifeng & Gao, Quanfu & Luo, Guanwei, 2020. "Two-parameter bifurcations of an impact system under different damping conditions," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Su, Han & Yue, Yuan & Liu, Run & Grebogi, Celso, 2024. "Crisis dynamics of a class of single-degree-of-freedom piecewise linear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    3. Li, Hong-guang & Meng, Guang, 2007. "Nonlinear dynamics of a SDOF oscillator with Bouc–Wen hysteresis," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 337-343.
    4. Yuan, Zi & Chen, Lincong & Sun, Jian-Qiao, 2025. "Stochastic dynamics of hysteresis systems under harmonic and Poisson excitations," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
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