Stability of a flexible link with an arbitrarily oriented tip rotor and a conservative tip load

A mathematical model of a uniform Bernoulli-Euler beam with a single discrete arbitrarily oriented rotor located at the tip of the beam is presented. The rotor is assumed to rotate at a constant angular velocity about its axis of inertial symmetry; that axis is not necessarily 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