Resonant vibration of shallow suspension footbridges

A cable-supported footbridge model with pre-tensioned cables in vertical and horizontal planes is proposed to investigate the vibration characteristics of shallow suspension footbridges under walking dynamic loads in this conceptual study. In this bridge model, the tension forces in the supporting cables can be adjusted by introducing pre-tensions to the reverse-profiled cables, and therefore the natural frequencies can be altered to cover the frequency range of dynamic forces induced by pedestrians. In the numerical analysis, SAP2000 is adopted to study the vibration properties and dynamic response under walking loads. The synchronous response of the bridge structure is stimulated by resonant vibration. The crowd walking loads are modelled as uniform loads acting on the whole bridge deck and they consist of three parts: vertical dynamic force, lateral dynamic force and vertical static force. Numerical results show that for a shallow suspension footbridge the lowest frequencies correspond to lateral and torsional vibration modes which are always combined together and become two types of coupled modes: coupled lateral–torsional modes, as well as coupled torsional–lateral modes. As an example, a bridge model with fundamental frequency of 0·75 Hz in the lateral direction has been studied. It is found that the vibration in the lateral direction is quite different from that in the vertical direction and that damping has significant effect on the vertical vibration but small effect on the lateral one. Moreover, vertical static load has significant effect on the lateral vibration when the bridge structure vibrated in coupled modes.