Keywords: train-bridge resonance, non-linear dynamic properties, dynamic assessment.

The amplitude dependency of the dynamic properties of a ballasted, single span, steel-concrete composite railway bridge and its influence on the structural response in a state of train-bridge resonance has been studied. In a state of resonance caused by train-bridge interaction, one single mode is often dominant. Therefore, a single-degree-of-freedom model can be satisfactory, at least as a first approximation. For a particular bridge, it has been shown that for accelerations between 0 and 0.3m/s², the stiffness decreases and the damping increases with increasing acceleration. However, the nature of the observed non-linear behaviour is not yet known and therefore it was treated in the sense of a "black box".

Experimentally determined natural frequency and damping ratio functions were introduced in a simple single-degree-of-freedom system to simulate the bridge response at resonance. A comparison of this simple model with the measured response showed that the proposed model is in reasonable agreement with the measured reality and hence, a study of the resonant behaviour using this model was motivated. However, several aspects regarding the nature of the non-linearities need to be further studied in order to use this type of model in a predictive manner. The main draw-back of the results presented is the limited range of movements from which the damping and frequency functions were determined and that they were determined from free vibrations, without the influence of the train. For example, a likely source of the observed non-linearities is soil-structure interaction. It is well known that the behaviour of soil materials is dependent not only on the state of strain, but also on the state of stress. The state of stress in the track superstructure and under the foundations in a state of train-bridge resonance is probably not well represented by that in free vibrations.

Nevertheless, some indications regarding the amplitude of vibration in a state of train-bridge resonance are discussed. Naturally, the increasing damping leads to a decrease in the resonant amplitude. This finding may, if further research geared towards an understanding of the phenomena which cause the observed behaviour is performed, lead to substantial savings for society in that capacity assessments of existing bridges can be made in a less conservative, but yet robust manner. In a longer perspective, work along this line may lead to the establishment of the bridge types which have this non-linear behaviour, and thereby less conservative choices of damping for predictive simulations also in the design stage. On the other hand, the fact that the natural frequency decreases with the amplitude of vibration may lead to an overestimated critical train speed which also motivates further research.

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