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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).
