Non-potential dissipative systems exhibiting periodic attractors in regions of divergence

The dynamics of non-conservative dissipative systems, under partial follower loading, in regions of divergence (static) instability is thoroughly reexamined. Such autonomous non-potential systems are discussed as: (a) perfect bifurcational systems with trivial fundamental paths, and (b) imperfection sensitive (or limit point) systems. For systems (a), the conditions under which the loss of stability is due either to a Hopf bifurcation (purely imaginary eigenvalues) or to a double zero eigenvalue are properly established. New phenomena (i.e. equilibria associated with periodic attractors, flutter instability occurring prior to divergence, disappearance of the region of flutter instability, destabilization near the double branching point, etc.) are discovered contradicting existing and widely accepted results based on classical analyses. For systems (b), energy and topological criteria related to the dynamic buckling mechanism are comprehensively presented. These criteria allow us to establish readily exact and approximate dynamic buckling loads of excellent accuracy for structural design purposes. The theoretical findings are verified via a variety of numerical results of two models, of two and three degrees of freedom.