A dynamic model for a rotating beam subjected to axially moving forces

This paper presents a dynamic model for the vibration of a rotating Timoshenko beam subjected to a three-directional load moving in the axial direction. The model takes into account the axial movement of the axial force component. The bending moment produced by this component acting on the surface of the beam is included in the model. The two other transverse force components are either of constant magnitude or a linear function of the local deflection. Lagrangeʹs equations of motion for the modal coordinates are derived based on the assumed mode method. These equations are then solved by a fourth-order Runge–Kutta algorithm. Numerical examples are analysed. The effects of the axial force component and its induced bending moment, and the deflection-dependence of the moving forces on the dynamic behaviour of the system at various travelling speeds are investigated. It is found that the bending moment induced by the axial force component has a significant influence on the dynamic response of the rotating beam and hence must be considered in such problems as turning operations.