Vibration of multi-span non-uniform bridges under moving vehicles and trains by using modified beam vibration functions

Abstract Based on the Lagrangian approach, the vibration of a multi-span non-uniform bridge subjected to a moving vehicle is analyzed by using modified beam vibration functions as the assumed modes. The vehicle is modelled as a two-degree-of-freedom system. The method is extended to the action of a moving train by modelling it as a series of two-degree-of-freedom systems. All the derived formulae are expressed in matrix form and therefore programming is quite straightforward. The total number of unknowns for this method is very small compared with that of the finite element method. Convergence is very quick and in almost all cases 12–16 terms are sufficient to give satisfactory results.

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