An. Kounadis et al., ON THE RELIABILITY OF CLASSICAL DIVERGENCE INSTABILITY ANALYSES OF ZIEGLER NONCONSERVATIVE MODEL, Computer methods in applied mechanics and engineering, 95(3), 1992, pp. 317-330
The critical states of divergence instability of the two-degree-of-fre
edom Ziegler's model under a nonconservative follower load are reexami
ned with the aid of a nonlinear static and dynamic analysis. The long-
term postcritical response is studied by discussing the effect of vari
ous parameters such as geometric and stiffness nonlinearities, linear
viscous damping and initial geometric imperfections. To this end the s
tability of equilibria and limit cycles is explored with the aid of gl
obal solutions based on the original nonlinear equations of motion in
order to include nonperiodic (chaotic) motion phenomena. New important
results obtained by nonlinear static and dynamic analyses contradict
existing findings based on classical linearized solutions. It is found
that the critical load coincides with the corresponding dynamic one (
associated with a divergent motion) only for models without precritica
l deformations. Some chaoslike phenomena of dissipative or non-dissipa
tive autonomous systems due to competing equilibrium point attractors
are also presented.