Modal analysis of tower-cable system of Tsing Ma long suspension bridge

A three-dimensional dynamic finite element model is established for the tower-cable system of the Tsing Ma long suspension bridge which is currently under construction. The two bridge towers, made up of reinforced concrete columns and deep prestressed concrete beams, are modelled by three-dimensional Timoshenko beam elements with rigid arms at the connections between columns and beams. The main span and side span cables are modelled by three-node cable elements accounting for geometric nonlinearity and large elastic deflection. The modal analysis is then performed to determine the dynamic characteristics and dynamic interaction between the towers and cables. The results show that at lower natural frequencies, the modes of vibration of the system can be reasonably separated into in-plane modes and out-of-plane modes. Dynamic interactions between the towers and cables are significant at global natural frequencies in either in-plane or out-of-plane vibration. There are many local natural frequencies at which the cables vibrate but the towers remain stationary or have relatively small modal motion only. The dynamic interactions between the main span and side span cables are also observed at some local natural frequencies. The finite element model and the analytical results presented in this paper have been verified by measuring the dynamic properties of the system.