Nonlinear cable-deck interaction vibrations of cable-stayed bridges

In modern cable-stayed bridges, cables connect with other components such as the bridge deck and dynamic interactions occur between the cables and the rest of the structure. When the natural frequencies of a global vibrational mode and a cable mode are close, there can be significant interactions between the cable and deck. This can lead to vibration behaviour different to that of a simple cable-only dynamic system and hence vulnerability to cable fatigue or overloading. In this paper, a nonlinear cable-supported model is introduced. This model of one cable attached at the top of the deck allows for cable inclination, small sagging and multiple vibrational modes in two planes. Using scaling and averaging methods, analytical solutions in the form of non-dimensional polynomial equations have been derived for the steady state vibration amplitudes of the deck and cable of the coupled system. This analysis reveals a significant two resonance peak phenomenon which is not apparent from simpler cable-only analyses. Moreover, the feedback of the cable not only influences the cable response stability, but also the vibration amplitude of the cable and deck response. Results are presented for a typical inclined bridge cable interacting with a deck excited by the external force on the deck, highlighting the strong effect of the mass ratio between the cable and deck on the cable-deck interaction performance. The feedback of the cable vibration on the deck and cable response is non-negligible even for a relatively large mass ratio. Therefore, for practical cable-stayed bridges the interaction between cable and deck needs to be considered to obtain an accurate dynamic response in some cases.