On the stability and instability regions of nonconservative continuous system under partially follower forces

The transition between stability and instability of a uniform cantilever beam subjected to a partially follower load is discussed by means of the finite element method. The stability diagram in terms of the load versus the non-conservativeness loading parameter is obtained both in the hypothesis of linearized (small displacements) and non-linearized (large displacements) analysis. It is found that the regions of divergence and flutter instability of the finite element model of continuous system are quite different from the corresponding ones obtained for the classical 2 degrees of freedom Ziegler's model (i.e. the inverted double pendulum), both quantitatively and qualitatively. The transition from the 2 degrees of freedom model to the continuous model is investigated through the study of some multi degrees of freedom approximation models (i.e. the 3, 4, 5 and 10 degrees of freedom models) of the continuous column. Finally, the effect of damping in the stability diagram of the finite element model of continuous system is discussed and the destabilizing effect of small damping is emphasized.