Analytical-numerical studies on the stability and bifurcations of periodic motion in the vibro-impact systems with clearances

Xu, H; Ji, J

Analytical-numerical studies on the stability and bifurcations of periodic motion in the vibro-impact systems with clearances

Xu, H Ji, J

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Publication Type:: Journal Article
Citation:: International Journal of Non-Linear Mechanics, 2019, 109 pp. 155 - 165
Issue Date:: 2019-03-01

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Field	Value	Language
dc.contributor.author	Xu, H	en_US
dc.contributor.author	Ji, J https://orcid.org/0000-0003-3280-5463	en_US
dc.date.issued	2019-03-01	en_US
dc.identifier.citation	International Journal of Non-Linear Mechanics, 2019, 109 pp. 155 - 165	en_US
dc.identifier.issn	0020-7462	en_US
dc.identifier.uri	http://hdl.handle.net/10453/134877
dc.description.abstract	© 2018 This paper investigates the stability and bifurcations of periodic solutions in three-degree-of-freedom vibro-impact systems based on the explicit critical criteria and the discontinuous mapping method. Firstly, a six-dimensional Poincaré map is established by taking the impact surface as the Poincaré section. The explicit criteria including eigenvalue assignment and transversality condition are applied to determine the bifurcation point of co-dimension one pitchfork bifurcation. The stability and direction of the bifurcation solution are then studied by using center manifold reduction theory and normal form approach. Secondly, the bifurcation points of co-dimension-two Hopf–Hopf interaction bifurcation and pitchfork–Neimark–Sacker bifurcation are determined by applying the explicit critical criteria, and the local dynamic behaviors are examined in the neighborhood of these co-dimension-two bifurcation points. Finally, a six-dimensional Poincaré map formed by choosing the constant phase angle as the Poincaré section is used to investigate the existence and stability of grazing bifurcation based on the piecewise compound normal form map. The causes of the discontinuous jump and the coexistence of attractors near the grazing periodic motion are explained for the three-degree-of-freedom vibro-impact system with a moving constraint.	en_US
dc.relation.ispartof	International Journal of Non-Linear Mechanics	en_US
dc.relation.isbasedon	10.1016/j.ijnonlinmec.2018.11.003	en_US
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject.classification	Mechanical Engineering & Transports	en_US
dc.title	Analytical-numerical studies on the stability and bifurcations of periodic motion in the vibro-impact systems with clearances	en_US
dc.type	Journal Article
utslib.citation.volume	109	en_US
utslib.for	0913 Mechanical Engineering	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0905 Civil Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	closed_access	*
pubs.publication-status	Published	en_US
pubs.volume	109	en_US

Abstract:

© 2018 This paper investigates the stability and bifurcations of periodic solutions in three-degree-of-freedom vibro-impact systems based on the explicit critical criteria and the discontinuous mapping method. Firstly, a six-dimensional Poincaré map is established by taking the impact surface as the Poincaré section. The explicit criteria including eigenvalue assignment and transversality condition are applied to determine the bifurcation point of co-dimension one pitchfork bifurcation. The stability and direction of the bifurcation solution are then studied by using center manifold reduction theory and normal form approach. Secondly, the bifurcation points of co-dimension-two Hopf–Hopf interaction bifurcation and pitchfork–Neimark–Sacker bifurcation are determined by applying the explicit critical criteria, and the local dynamic behaviors are examined in the neighborhood of these co-dimension-two bifurcation points. Finally, a six-dimensional Poincaré map formed by choosing the constant phase angle as the Poincaré section is used to investigate the existence and stability of grazing bifurcation based on the piecewise compound normal form map. The causes of the discontinuous jump and the coexistence of attractors near the grazing periodic motion are explained for the three-degree-of-freedom vibro-impact system with a moving constraint.

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http://hdl.handle.net/10453/134877