ON THE RELATION OF STATIC TO DYNAMIC BIFURCATION IN NONLINEAR AUTONOMOUS DISSIPATIVE OR NONDISSIPATIVE STRUCTURAL SYSTEMS

MAHRENHOLTZ, O; KOUNADIS, AN

dc.contributor.author	MAHRENHOLTZ, O	en
dc.contributor.author	KOUNADIS, AN	en
dc.date.accessioned	2014-03-01T01:42:14Z
dc.date.available	2014-03-01T01:42:14Z
dc.date.issued	1993	en
dc.identifier.issn	0044-2267	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/23723
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mechanics	en
dc.subject.other	CHAOSLIKE PHENOMENA	en
dc.subject.other	STABILITY	en
dc.title	ON THE RELATION OF STATIC TO DYNAMIC BIFURCATION IN NONLINEAR AUTONOMOUS DISSIPATIVE OR NONDISSIPATIVE STRUCTURAL SYSTEMS	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1993	en
heal.abstract	Dynamical dissipative or nondissipative discrete systems under constant directional (conservative) step loading described by nonlinear autonomous Ordinary Differential Equations (ODEs) are considered. Attention is restricted on gradient structural systems which under the same loading applied statically exhibit a branching point critical response bifurcating from a trivial prebuckling path. The connection of static bifurcations and stability with the corresponding dynamic bifurcations and stability are comprehensively discussed after a thorough investigation of the structural form of the Jacobian matrix and its characteristic equation. The relation of the eigenvalues of the statical system with those of the dynamical system associated with the Jacobian matrix is examined at the precritical, critical and posteritical stage. This enables us to establish very simple stability conditions (related basically to the sign of second variation of the total potential energy) compared to those of Routh-Hurwitz.	en
heal.publisher	AKADEMIE VERLAG GMBH	en
heal.journalName	ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK	en
dc.identifier.isi	ISI:A1993KT77100001	en
dc.identifier.volume	73	en
dc.identifier.issue	3	en
dc.identifier.spage	131	en
dc.identifier.epage	140	en