The Influence of Combined Concentrated and Distributed Follower Forces on the Eigensolutions of A Spinning Beam

The free vibrations of a spinning Timoshenko beam under the action of the non-conservative follower forces are solved analytically for the first time. Three types of follower-force system are considered: concentrated follower forces, distributed follower forces and, combined concentrated and distributed follower forces. The resulting characteristic equation for computing frequencies is very complicated and a novel solution algorithm involving symbolic algebraic operations with each term determined recursively, is proposed. Critical values of the concentrated follower forces that correspond to the onset of the flutter-type instability for the first four modes of vibration are presented.