An. Kounadis, CRITERIA FOR OCCURRENCE OF FLUTTER INSTABILITY BEFORE BUCKLING IN NONCONSERVATIVE DISSIPATIVE SYSTEMS, AIAA journal, 35(3), 1997, pp. 509-518
The occurrence of flutter instability through a Hopf bifurcation befor
e static buckling in regions of divergence in nonconservative, nonself
-adjoint, dissipative systems is thoroughly discussed using a qualitat
ive analysis. This region where both Ziegler's and static criterion ma
y fail to predict the actual critical load is defined via two values (
bounds) of the nonconservativeness loading parameter eta; the upper bo
und corresponds to eta = 0.5 (being invariant with respect to all othe
r parameters), whereas the lower bound corresponds to a double critica
l (divergence) point beyond which there are no adjacent equilibria. Th
e location of the last point (lying always between eta = 0 and 0.5) de
pends on a stiffness parameter. It is also found that the region of no
nexistence of adjacent equilibria becomes maximum (minimum) when the d
ouble critical point corresponds to eta = 0.5 (eta = 0). The interacti
on 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.