Abstract
The present work discuss the local dynamic asymptotic stability of 2-DOF weakly damped nonconser-vative systems under follower compressive loading in regions of divergence, using the Lienard–Chipartstability criterion. Individual and coupling effects of the mass and stiffness distributions on the localdynamic asymptotic stability in the case of infinitesimal damping are examined. These autonomoussystems 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 diver-gence (static) instability of systems with positive definite damping matrices. The aforementioned massand stiffness parameters combined with the algebraic structure of positive definite damping matrices mayhave under certain conditions a tremendous effect on the Jacobian eigenvalues and thereafter on the localdynamic asymptotic stability of these autonomous systems. It is also found that contrary to conservativesystems local dynamic asymptotic instability may occur, strangely enough, for positive definite dampingmatrices before divergence instability, even in the case of infinitesimal damping (failure of Ziegler’skinetic criterion).
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