Criteria for occurrence of flutter instability before buckling in nonconservative dissipative systems

Abstract

The occurrence of flutter instability through a Hopf bifurcation before static buckling in regions of divergence in nonconservative, nonself-adjoint, dissipative systems is thoroughly discussed using a qualitative analysis. This region where both Ziegler's and static criterion may fail to predict the actual critical load is defined via two values (bounds) of the nonconservativeness loading parameter η; the upper bound corresponds to η = 0.5 (being invariant with respect to all other parameters), whereas the lower bound corresponds to a double critical (divergence) point beyond which there are no adjacent equilibria. The location of the last point (lying always between η = 0 and 0.5) depends on a stiffness parameter. It is also found that the region of nonexistence of adjacent equilibria becomes maximum (minimum) when the double critical point corresponds to η = 0.5 (η = 0). The interaction of vanishing damping with various parameters leads to new phenomena related to point and periodic attractors as well as to a new type of dynamic bifurcation.