The effect of infinitesimal damping on the dynamic instability mechanism of conservative systems

Sophianopoulos, DS; Michaltsos, GT; Kounadis, AN

dc.contributor.author	Sophianopoulos, DS	en
dc.contributor.author	Michaltsos, GT	en
dc.contributor.author	Kounadis, AN	en
dc.date.accessioned	2014-03-01T01:29:19Z
dc.date.available	2014-03-01T01:29:19Z
dc.date.issued	2008	en
dc.identifier.issn	1024-123X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19219
dc.subject	Dynamic Instability	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.other	Asymptotic analysis	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Damping	en
dc.subject.other	Dynamic analysis	en
dc.subject.other	Hopf bifurcation	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Stability criteria	en
dc.subject.other	System stability	en
dc.subject.other	Algebraic structures	en
dc.subject.other	Applied loads	en
dc.subject.other	Autonomous System (AS)	en
dc.subject.other	Conservative systems	en
dc.subject.other	Constant magnitude	en
dc.subject.other	Coupling effects	en
dc.subject.other	Damped systems	en
dc.subject.other	Damping matrices	en
dc.subject.other	Degrees of freedom	en
dc.subject.other	Dynamic instabilities	en
dc.subject.other	Eigenvalues (of graphs)	en
dc.subject.other	Free-motion	en
dc.subject.other	Global asymptotic stability (GAS)	en
dc.subject.other	Individual (PSS 544-7)	en
dc.subject.other	Jacobian	en
dc.subject.other	Local instability	en
dc.subject.other	Local stability	en
dc.subject.other	Non linear dynamic analyses	en
dc.subject.other	Periodic motions	en
dc.subject.other	Stiffness distributions	en
dc.subject.other	Asymptotic stability	en
dc.title	The effect of infinitesimal damping on the dynamic instability mechanism of conservative systems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1155/2008/471080	en
heal.identifier.secondary	http://dx.doi.org/10.1155/2008/471080	en
heal.identifier.secondary	471080	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	The local instability of 2 degrees of freedom (DOF) weakly damped systems is thoroughly discussed using the Liénard-Chipart stability criterion. The individual and coupling effect of mass and stiffness distribution on the dynamic asymptotic stability due to mainly infinitesimal damping is examined. These systems may be as follows: (a) unloaded (free motion) and (b) subjected to a suddenly applied load of constant magnitude and direction with infinite duration (forced motion). The aforementioned parameters combined with the algebraic structure of the damping matrix (being either positive semidefinite or indefinite) may have under certain conditions a tremendous effect on the Jacobian eigenvalues and then on the local stability of these autonomous systems. It was found that such systems when unloaded may exhibit periodic motions or a divergent motion, while when subjected to the above step load may experience either a degenerate Hopf bifurcation or periodic attractors due to a generic Hopf bifurcation. Conditions for the existence of purely imaginary eigenvalues leading to global asymptotic stability are fully assessed. The validity of the theoretical findings presented herein is verified via a nonlinear dynamic analysis.	en
heal.publisher	HINDAWI PUBLISHING CORPORATION	en
heal.journalName	Mathematical Problems in Engineering	en
dc.identifier.doi	10.1155/2008/471080	en
dc.identifier.isi	ISI:000258127400001	en
dc.identifier.volume	2008	en