https://doi.org/10.1140/epjp/s13360-025-07205-z
Regular Article
Nonlinear vibro-impact dynamics induced by clearance and friction in a belt-driven oscillator
School of Mechatronic Engineering, Lanzhou Jiaotong University, 730070, Lanzhou, People’s Republic of China
a
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Received:
21
October
2025
Accepted:
11
December
2025
Published online:
27
January
2026
Abstract
A single-degree-of-freedom periodically forced oscillator with coupled clearance and friction nonlinearities is investigated. By analyzing the phase-space conditions governing free sliding, impact, and stick motion, and employing associated Poincaré maps, the dynamics of stick–slip periodic motions are systematically characterized. Particular emphasis is placed on the distribution and transition of periodic motions in the two-parameter space. The occurrence of bursting oscillations in the low-frequency region is revealed and the influence of key structural parameters on stick–slip behavior is examined. The results indicate that stick–slip motion predominantly occurs in regions characterized by low-frequency and small-clearance. Under the induction of grazing bifurcations, the transition toward stick motion is marked by an increase in the number of impacts, a decrease in impact velocity, and a contraction of the frequency band. The transitions between adjacent periodic motions are primarily governed by the synergistic effects of grazing, saddle-node, and sliding bifurcations. Owing to the irreversibility of the transition paths, multi-stability regions emerge, including co-existing states induced by grazing-(saddle-node), grazing-sliding, and doubling-sliding bifurcations. Furthermore, the increase in damping ζ suppresses multi-impact motions, resulting in improved system smoothness and stability along with reduced structural wear; however, it concurrently induces a rise in energy consumption.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
