Regulation of Bifurcations in QZS Vibration Isolators via Horizontal Dry Friction and Rotational Damping

Articles in Press

Document Type : Research Paper

Authors
Xuanzhi Bu
Jiangchuan Niu
Wanjie Zhang
School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
10.22055/jacm.2026.49134.5758
Abstract
Aiming to overcome the performance limitations of quasi-zero-stiffness (QZS) vibration isolators in the resonance band, a novel vibration isolation scheme incorporating horizontal dry friction and rotational damping is proposed. Lagrange’s equations and the averaging method are employed to establish the system’s dynamic model and examine its primary resonance, thereby deriving the amplitude-frequency relationship. The effects of nonlinear damping parameters on isolation performance are studied via comparative analysis, with the energy dissipation problem quantitatively revealed by power flow analysis. The role of system parameters in governing dynamic bifurcations is explored by employing a combined analytical framework of Poincaré maps and Floquet multipliers. Furthermore, an exploration of the global bifurcation dynamics is conducted via cell mapping theory. Findings demonstrate that relative to both the traditional QZS design and a QZS isolator incorporating horizontal damping, the new configuration exhibits superior vibration isolation performance within the resonance frequency band. Increasing rotational damping not only diminishes the peak magnitude but also reduces the range of saddle-node and period-doubling bifurcations while expanding the basin of attraction for small amplitudes. However, this enhancement increases force transmissibility at high frequencies. Conversely, increasing horizontal dry friction effectively reduces the resonance peak, broadens the isolation frequency band, and expands the basin of attraction for small amplitudes without elevating high-frequency force transmissibility. In addition, horizontal friction demonstrates superior energy dissipation effect in the low-frequency range but excessively high horizontal friction can induce period-doubling bifurcations within the system. Therefore, a moderate combination of horizontal dry friction and rotational damping yields the best overall isolation and stability.
Keywords
Quasi-zero stiffness
Vibration isolation
Dry friction
Bifurcation
Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Articles in Press, Corrected Proof
Available Online from 16 April 2026