ON THE RELIABILITY OF CLASSICAL DIVERGENCE INSTABILITY ANALYSES OF ZIEGLER NONCONSERVATIVE MODEL

The critical states of divergence instability of the two-degree-of-freedom Ziegler's model under a nonconservative follower load are reexamined with the aid of a nonlinear static and dynamic analysis. The long-term postcritical response is studied by discussing the effect of various parameters such as geometric and stiffness nonlinearities, linear viscous damping and initial geometric imperfections. To this end the stability of equilibria and limit cycles is explored with the aid of global 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 precritical deformations. Some chaoslike phenomena of dissipative or non-dissipative autonomous systems due to competing equilibrium point attractors are also presented.