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Vibration analysis of Timoshenko beams under uniform partially distributed moving masses

S. Ziaei-Rad, A. Ariaei, M. Imregun

Journal of Multi-body Dynamics, Vol. 221, Part K, pp. 1-16, 2007



The current article presents an analytical approach, as well as a calculation method for determining the dynamic response of Timoshenko beams under uniform partially distributed moving masses, using the so-called discrete element technique (DET). It is shown that the proposed methodology offers a compact and computationally efficient way of conducting parametric studies to evaluate the dynamic response of the beam-like structures with arbitrary boundary conditions such as railway and road bridges. First, a formulation is presented in a matrix form for beams under partially distributed masses. The results have been validated against analytical formulations, finite difference, and finite element results. A number of parametric studies were conducted to assess the effects of the moving mass velocity and moving mass length on the beam deflection. A major aspect of the work is the study of successive travelling masses for which the transient effects are important. Both analytical and DET results showed that the critical speeds were affected for successive moving masses. Finally, the effects of rotary inertia were studied for a range of inertia values to quantify the error arising from using the Bernoulli-Euler formulation for beams with large inertias.



moving distributed masses successive masses rotary inertia critical travelling speed discrete element technique


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