In this paper, differential quadrature element method (DQEM) is used to study vibration analysis of multi-span Timoshenko beams with non-uniform thickness and general boundary conditions. In order to generalize the boundary conditions at two ends of the beam, each support is moulded using two springs; a translational and a rotational; also interior supports are considered as simple supports. Governing equations, compatibility conditions at each constraint point and external boundary conditions are derived and formulated using DQEM. The compatibility conditions are considered as continuity in bending moment and rotation due to the bending; as well vertical displacement is equal to zero. Accuracy, convergence and versatility of the proposed solution are confirmed using exact solution presented by other authors and effect of quantity and position of interior supports on natural frequencies are investigated. Because the proposed solution is quicker in comparison with the previous presented methods and can be used even for beams with high number of supports, solution acquired by this method is new and efficient. In addition, presented solution is able to analyze vibration of the multi-span beams with non-uniform thickness which is difficult or sometimes impossible to be solved with exact approaches. The achieved results show that existence of the interior supports leads to increase in all natural frequencies and value of this rise depends on the position of these supports.

vibration, non-uniform thickness, multi-span beam, differential quadrature element method (DQEM).