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

An idealized mathematical model of a uniform Bernoulli-Euler beam with a single discrete rotor located at the tip of the beam is presented. The rotor is assumed to rotate at a constant angular velocity and to have an axis of inertial symmetry which is coincident with the neutral axis of the beam. The governing equations of motion are derived when, the system is subject to a compressive conservative external load. 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