Theoretical model and numerical simulation of tower-wake-induced vibration of a flexible suspender

For a suspension bridge, suspenders in the wake of bridge tower interfered by the shedding vortices, would experience a large-amplitude vibration, named as tower-wake-induced vibration (TWIV). At specific wind speeds, the vibrating frequency of suspenders during TWIV would be captured by the shedding frequency of the tower wake, which is the lock-in of TWIV. The present research establishes the governing equations of flexible suspenders, considering the tension variations caused by the deformation, also adopts the aerodynamic model of TWIV, to study the lock-in phenomenon and the TWIV characteristics. To explore the variation trend of nonlinear frequency with amplitude of suspenders, the difference of dynamic parameters of suspenders in two vibrating motions are recognized through free vibration motions at first. Then, a formula for the equivalent amplitude-dependent (EAD) frequency of the suspender is raised. The lock-in phenomenon of TWIV is reproduced in these two motions as well. Eventually, TWIVs of four suspenders at various positions in the rear of bridge tower are simulated based on practical engineering, considering the variation of aerodynamic forces along the altitude due to the wind profile. The conclusions indicate that TWIV of suspenders is a low-frequency and low-order-mode vibration at high wind speeds.