Dynamic response of a rotating multi-span shaft with general boundary conditions subjected to a moving load

This paper investigates the dynamic response of a rotating multi-span shaft with general boundary conditions subjected to an axially moving load. The system equations of motion are derived based on the global assumed mode method and a modified transformation matrix is proposed to deal with the multi-span geometric constraints. The numerical results are solved by the Runge–Kutta method. To ensure the validity of the method, the convergence test for dynamic response and the comparison of natural frequencies obtained by both the present method and finite element method are demonstrated. Numerical simulations are performed to study the effects of the moving speed of the load, the number of spans, and the rotational speed of the shaft on the deflections under the moving load. In addition, the effects on the occurring position of maximum deflection are presented. The numerical results show that the maximum deflection in the direction of the load may occur at any span and near the midpoint of one span. However, the maximum deflection induced by the gyroscopic effect in the direction perpendicular to the load always occurs at the first span. Moreover, the occurring position of maximum deflection is independent of the rotational speed.