Conditions for the occurrence of limit cycles in autonomous potential damped systems

Kounadis, AN; Sophianopoulos, DS

dc.contributor.author	Kounadis, AN	en
dc.contributor.author	Sophianopoulos, DS	en
dc.date.accessioned	2014-03-01T01:14:28Z
dc.date.available	2014-03-01T01:14:28Z
dc.date.issued	1999	en
dc.identifier.issn	0020-7462	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13091
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0008440751&partnerID=40&md5=94037c47e0f985ea2c8f09119a2d4a0d	en
dc.subject	Autonomous discrete systems	en
dc.subject	Dynamic stability	en
dc.subject	Limit cycles	en
dc.subject	Symmetric/asymmetric damped systems	en
dc.subject	Symmetrizable matrices	en
dc.subject.classification	Mechanics	en
dc.subject.other	NONCONSERVATIVE SYSTEMS	en
dc.subject.other	DISSIPATIVE SYSTEMS	en
dc.subject.other	INSTABILITY	en
dc.subject.other	DIVERGENCE	en
dc.subject.other	REGIONS	en
dc.title	Conditions for the occurrence of limit cycles in autonomous potential damped systems	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1999	en
heal.abstract	The focal dynamic stability of discrete, weakly damped, systems under step loading of infinite duration either constant directional (potential load) or partial follower (non-potential load) is thoroughly re-examined. In particular, for such autonomous damped systems we seek conditions for the existence of: (a) a limit cycle response in case of a potential loading (symmetric) system and (b) a non-singular transformation which transforms a non-potential (asymmetric) system into an equivalent symmetric system. Using a 2-DOF as a model new findings are established that contradict existing widely accepted results. Thus, symmetric systems under certain conditions can exhibit a limit cycle response due to either a double-zero Jacobian eigenvalue or to a Hopf bifurcation. Also asymmetric (non-self-adjoint) systems, regardless of the degree of asymmetry, can always be transformed into equivalent symmetric systems. A variety of numerical examples confirm the validity of the theoretical findings presented herein. (C) 1999 Elsevier Science Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Non-Linear Mechanics	en
dc.identifier.isi	ISI:000080105900014	en
dc.identifier.volume	34	en
dc.identifier.issue	5	en
dc.identifier.spage	949	en
dc.identifier.epage	966	en