Vol. 4, No. 7-8, 2009

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ISSN: 1559-3959
The effect of infinitesimal damping on nonconservative divergence instability systems

Anthony N. Kounadis

Vol. 4 (2009), No. 7-8, 1415–1428
Abstract
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The present work discuss the local dynamic asymptotic stability of 2-DOF weakly damped nonconservative systems under follower compressive loading in regions of divergence, using the Liénard–Chipart stability criterion. Individual and coupling effects of the mass and stiffness distributions on the local dynamic asymptotic stability in the case of infinitesimal damping are examined. These autonomous systems may either be subjected to compressive loading of constant magnitude and varying direction (follower) with infinite duration or be completely unloaded. Attention is focused on regions of divergence (static) instability of systems with positive definite damping matrices. The aforementioned mass and stiffness parameters combined with the algebraic structure of positive definite damping matrices may have under certain conditions a tremendous effect on the Jacobian eigenvalues and thereafter on the local dynamic asymptotic stability of these autonomous systems. It is also found that contrary to conservative systems local dynamic asymptotic instability may occur, strangely enough, for positive definite damping matrices before divergence instability, even in the case of infinitesimal damping (failure of Ziegler’s kinetic criterion).

Keywords
nonconservative divergence, follower load, infinitesimal damping mass, Liénard–Chipart criterion, asymptotic instability
Milestones
Received: 12 September 2008
Revised: 27 January 2009
Accepted: 5 February 2009
Published: 26 December 2009
Authors
Anthony N. Kounadis
Foundation for Biomedical Research
Academy of Athens
Soranou Efessiou 4
11527 Athens
Greece