The stability of a flexible link with a tip rotor and a compressive tip load

A mathematical model of a Euler-Bernoulli beam with a discrete gyroscopic element, consisting of a single rotor located at the tip of the beam, is presented. The rotor is assumed to have a constant angular velocity and an axis of inertial symmetry which is coincident with the neutral axis of the beam. The governing equations of motion and corresponding boundary conditions are derived when the system is subject to conservative external loads. It is shown that these systems can display both static instabilities (divergence) and dynamic instabilities (flutter), that the structure of the stability regions depends on the distribution of stiffness and that gyroscopic stabilization is sometimes possible