Geometric stiffening of Timoshenko beams

The equations of motion of a prismatic isotropic Timoshenko beam with a tip mass and attached to a rotating hub are derived including the effects of centrifugal forces which appear in the equations of motion as nonlinear functions of the angular speed. The Rayleigh-Ritz method is used to obtain approximate solutions for the cases of a prescribed torque profile and a prescribed hub angular speed profile. In the case of a constant torque input, the effect of the centrifugal forces is not observed until sufficient angular speed is reached. When the system is driven under a constant velocity, it is observed that, for a sufficiently high angular speed, the centrifugal forces reduce the vibration amplitude.