Stability of weakly-damped systems under follower loads exhibiting Hopf bifurcations

Abstract

The existence of flutter instability through a Hopf (degenerate or generic) bifurcation prior to divergence (static) instability of Ziegler’s cantilever, weakly-damped models under partial follower compressive tip load (autonomous systems) is thoroughly discussed. Attention is focused on establishing the locus of the above dynamic bifurcations in regions of divergence defined by the nonconservative loading parameter η. The local as well as the global nonlinear dynamic instability of such bifurcations is conveniently established using the Runge–Kutta numerical scheme. Several examples for a variety of values of parameters will demonstrate the proposed technique as well as the new findings presented herein.