Numerical Study on Broadband Vibration Reduction of Ultra-Long Stay Cables by a Hybrid Countermeasure: A Viscous Damper and Tuned Mass Dampers

Due to the high slenderness ratio, low damping and small mass, ultra-long stay cables are extremely prone to several kinds of wind-induced vibrations, such as rain-wind induced vibration (RWIV) and vortex-induced vibration (VIV). For ultra-long stay cables, a single viscous damper (VD) is difficult to simultaneously mitigate the low-order RWIV and high-order VIV. In this study, a new hybrid method including a VD and tuned mass dampers (TMDs) to reduce broadband vibrations of ultra-long stay cable is proposed. First, the motion equation of the cable-VD-TMDs system is established, and the complex eigenvalues of the motion equation are numerically solved to analyze the dynamic characteristics of the cable-VD-TMDs system. Second, a series of two parametric analyses of the cable-TMD system, focusing on the damping ratio of the tuning mode of the stay cable, are conducted to systematically investigate the effect of the mass, frequency, tuning damping and the installation position of the TMD. Based on the parametric analyses of one single TMD, two TMDs are optimized to increase the modal damping ratio of two node modes of the cable-VD system. Finally, the sensitivity of the optimized TMD parameters for the targeted node modes is also discussed. The results show that the numerical method proposed in this study is applicable to the dynamic characteristics analysis of the cable-VD-TMDs systems without the limitation of the number and the installation positions of the dampers. TMDs can be used to successfully compensate for the shortcomings of the node modes for the cable-VD system. However, the coupling effect between the VD and the TMDs is not a linear superposition relationship because increasing the mass of the TMD reduces the sensitivity of the frequency, the tuning damping and the installation position of the TMD. The parameter optimization of TMDs is necessary to implement the wideband vibration reduction of the ultra-long stay cables.