Influence of non-linear stiffness and damping on the train-bridge resonance of a simply supported railway bridge

Previous experimental work has identified variations in the natural frequency and the modal damping ratio of the first vertical bending mode of vibration of a simply supported, single span steel–concrete composite bridge. It was found that the natural frequency decreased and the modal damping ratio increased with increasing amplitudes of vibration. This paper illustrates the influence of these variations on the train-bridge resonance of this particular bridge by means of a non-linear single degree of freedom system, based on the previously mentioned experimental results. As one might expect, the results indicate that the influence of the increasing damping ratio leads to a considerable decrease in the resonant amplitude whilst the decreasing natural frequency decreases the critical train speed at which resonance occurs. Further studies along this line of research may help us reduce the uncertainties in dynamic assessments of existing bridges based on dynamic measurements and improve our understanding of the dynamic properties of railway bridges in general.