Bifurcation structures and bursting dynamics in a two degrees of freedom quasi-zero stiffness system with elastic constrain

Chengyue Xing, Zhengdi Zhang and Miao Peng

Chaos, Solitons & Fractals, 2022, vol. 161, issue C

Abstract: In this manuscript, bifurcation structures and bursting patterns involving grazing phenomena are discussed based on a nonsmooth quasi-zero stiffness vibration isolation system. Within the selected parameter zone, analysis about stability and bifurcations of equilibria belonging to two sub-systems in phase space show that, equilibria of both sub-systems lose their stability through supercritical Hopf bifurcations. Numerical continuation performed on two sub-systems indicates that, the sub-system S− presents bi-stability consisting of small amplitude cycle branch circling around the S-shape equilibrium curve and large amplitude cycle branch, while the sub-system S+ presents mono-stability. Meanwhile, both cycle branches are terminated by fold bifurcations of cycle. Furthermore, as the quasi-static external force changes, periodic motions governed by the small amplitude branch of S− and cycle branch of S+ may touch the nonsmooth boundary and enter the other side of the boundary, which indicates the grazing bifurcations. By computing the bifurcation diagrams of the overall system, it is shown that grazing bifurcations result in complex distribution of cycle attractors as well as the occurrence of chaos. Based on these, multiple patterns of periodic and aperiodic bursting and the corresponding generation mechanisms are obtained. Besides, it is found that increasing the damping in coupling parts can improve the isolation efficiency.

Keywords: Quasi-zero stiffness system; Elastic constrain; Grazing bifurcation; Bursting (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922005343
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005343

DOI: 10.1016/j.chaos.2022.112324

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().