A NOVEL MODEL FOR PEDESTRIAN-INDUCED LATERAL VIBRATION OF FOOTBRIDGES—THE IP-K MODEL

The mechanism of pedestrian-induced lateral vibration of footbridges remains unclear and is accompanied by many controversies and deficiencies. Two main models are frequently used to explain the large lateral vibration of footbridges, that is, the synchronization locking model and the inverted pendulum model. The synchronous locking model indicates that a crowd on a bridge gradually adjusts their walking frequency and synchronizes ("lock-in") with the movement of the bridge, resulting in large lateral vibration of the bridge. By contrast, the inverted pendulum model supposes that the synchronization generated by the crowd adjusting the step frequency is not a prerequisite for the large lateral vibration of the bridge and asserts that the self-excited force caused by the pedestrian-bridge interaction is sufficient to cause vibrational instability, even if the pedestrians do not adjust the step frequency. Currently, the inverted pendulum model is considered more universal, but a debatable problem remains. The coefficient of component in phase with velocity c_\rm p under a normal walking frequency obtained by the inverted pendulum model is considerably less than the measured value. The reason for this problem is most likely that the inverted pendulum model ignores the real synchronization effect in practice. On this basis, a novel model for the pedestrian-induced lateral vibration of footbridges, namely, the inverted pendulum–Kuramoto model, is proposed, in which the inverted pendulum model is regarded as the core framework and the Kuramoto model is introduced into the inverted pendulum model to consider the synchronization effect between the crowd and the bridge vibration. In such a manner, the inverted pendulum model is improved to be more reasonable and closer to reality. The proposed model is applied to the north span of the Millennium Bridge to verify its effectiveness. Meanwhile, the influences of crucial parameters, including the walking frequency distribution, the number of pedestrians, and the sensitivity coefficient of pedestrians to the bridge amplitude, on c_\rm p are discussed in detail. A criterion for general linear instability/stability is established. The proposed model provides a powerful theoretical basis for revealing the mechanism of pedestrian-induced lateral vibration of footbridges.