On the failure of static stability analyses of nonconservative systems in regions of divergence instability

Kounadis, AN

dc.contributor.author	Kounadis, AN	en
dc.date.accessioned	2014-03-01T01:10:00Z
dc.date.available	2014-03-01T01:10:00Z
dc.date.issued	1994	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11292
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0028483807&partnerID=40&md5=9ae7bf0898aa00f182fc07e40bfb0b2f	en
dc.subject.classification	Mechanics	en
dc.subject.other	Buckling	en
dc.subject.other	Damping	en
dc.subject.other	Differential equations	en
dc.subject.other	Dynamics	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Loads (forces)	en
dc.subject.other	System theory	en
dc.subject.other	Systems analysis	en
dc.subject.other	Divergence instability	en
dc.subject.other	Double zero Jacobian eigenvalue	en
dc.subject.other	Hopf bifurcation	en
dc.subject.other	Nonconservative systems	en
dc.subject.other	Perfect bifurcational discrete dissipative systems	en
dc.subject.other	Static stability	en
dc.subject.other	System stability	en
dc.title	On the failure of static stability analyses of nonconservative systems in regions of divergence instability	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1994	en
heal.abstract	The stability of perfect bifurcational discrete dissipative systems under follower loads in regions of existence/non-existence of adjacent equilibria is thoroughly re-examined in the light of recent progress in nonlinear dynamics. A general theory for such nongradient systems described by autonomous ordinary differential equations is developed. Conditions for the existence of adjacent equilibria, the stability of precritical, critical and postcritical states, as well as for different types of local bifurcations are established. Focusing attention on the interaction of geometric nonlinearities and vanishing damping, new findings contradicting widely accepted results of the classical (linear) analysis are discovered. In a small region of adjacent equilibria near a compound branching point, which is explicitly determined, an interaction of two consecutive postbuckling modes occurs related to the following phenomena : in case of vanishing damping, loss of stability may occur via a Hopf (dynamic) bifurcation prior to static (divergence) buckling. Moreover, the critical states of divergence instability may be associated with a double zero Jacobian eigenvalue satisfying also the conditions of a Hopf (local) bifurcation. Besides local (dynamic) bifurcations, global bifurcations are also found. An example is used to illustrate the qualitative findings. © 1994.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Solids and Structures	en
dc.identifier.isi	ISI:A1994NT66600005	en
dc.identifier.volume	31	en
dc.identifier.issue	15	en
dc.identifier.spage	2099	en
dc.identifier.epage	2120	en