Double grazing periodic motions and bifurcations in a vibroimpact system with bilateral stops
type: Item
instance of: scholarly article
title: Double grazing periodic motions and bifurcations in a vibroimpact system with bilateral stops
zbMATH Open document ID: 1474.70040
DOI: 10.1155/2014/642589
author: Q.-H Li
author: Limei Wei
author: Jieyan Tan
author: Jiezhen Xi
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: The double grazing periodic motions and bifurcations are investigated for a two-degree-of-freedom vibroimpact system with symmetrical rigid stops in this paper. From the initial condition and periodicity, existence of the double grazing periodic motion of the system is discussed. Using the existence condition derived, a set of parameter values is found that generates a double grazing periodic motion in the considered system. By extending the discontinuity mapping of one constraint surface to that of two constraint surfaces, the Poincaré map of the vibroimpact system is constructed in the proximity of the grazing point of a double grazing periodic orbit, which has a more complex form than that of the single grazing periodic orbit. The grazing bifurcation of the system is analyzed through the Poincaré map with clearance as a bifurcation parameter. Numerical simulations show that there is a continuous transition from the chaotic band to a period-1 periodic motion, which is confirmed by the numerical simulation of the original system.
Mathematics Subject Classification ID: 70K50
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 70B15
zbMATH DE Number: 7022810
Wikidata QID: Q59040300
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/642589
OpenAlex ID: W2026177230
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description: scientific article; zbMATH DE number 7022810