Dynamic response of a multi-span Timoshenko beam with internal and external flexible constraints subject to a moving mass

An analytical transfer matrix method is presented to determine the effect of intermediate flexible constraints on the dynamic behavior of a multi-span beam subject to a moving mass. By using the Timoshenko beam theory on separate beams and applying the compatibility requirements on each constraint point, the relationships between every two adjacent spans can be obtained. By using a transfer matrix method, eigensolutions of the entire system can be determined. The forced responses can then be calculated by the modal expansion theory using the determined eigenfunctions. Some numerical results are presented to show the effects of intermediate constraints and locations on the dynamic response of the multi-span beams. It will be seen that the general formulation developed here can cover a large array of problems such as cracked or intermediately constrained beams.