The effect of infinitesimal damping on nonconservative divergence instability systems

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).