Vibration of a beam resting on movable supports and subjected to moving loads

摘要

The paper derives the equations for a beam subjected to a row of moving forces and simultaneous vertical motions of its supports. The very simple mathematical model is set up and the decomposition method is applied to the problem. The simply supported beam represent short to medium span bridge. The train effect consists of a long sequence of axle forces or their groups in regular distances, which can bring the bridges intensive vibration. The earthquake is idealized as a finite sum of harmonic movements of individual supports modulated by a slowly variable function. The numerical calculations were performed for both the concrete and steel bridges of spans 5 to 50 m subjected to the three types of high-speed trains (ICE, Eurostar/TGV and Talgo AV2) running at speeds 5 to 250 km/h. Influence of synchronization of train and earthquake attack is briefly analyzed. The effect of several other parameters is shown and discussed.