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Stay cables are becoming slender and their fundamental frequencies are becoming lower with the span of bridges increasing, thus leading to the occurrence of multi-modal vibration under various excitations. As a simple and effective strategy for cable vibration mitigation, the external damper is widely used in practice. However, one damper normally can target only fewer modes and poses limited effects on the control of multi-modal vibration. This paper proposed the use of a joint control system combining a viscous damper and a tuned mass damper for mitigating the multi-modal vibration of stay cables, followed by the optimization methodology of tuning and positioning. The control performance of the joint system was evaluated by numerical simulations. The feasibility of the joint control system was validated by analyzing the results of the comparative study, therefore providing a possible solution to multi-modal and high-modal vibration of stay cables.

The objective of this study is to thoroughly investigate the dynamic characteristics of the Kao Ping Hsi Bridge located in southern Taiwan. A one-element cable system (OECS) and a multi-element cable system (MECS) are presented for simulating the dynamic properties of the cables of the bridge. By a finite element computation procedure, the initial shape, modal, and seismic analyses are conducted for the bridge using either the OECS or MECS model. A hybrid method combining both the two-loop iteration and the catenary function is proposed to determine the initial shapes using the MECS model. Convergent and smooth initial shapes can be obtained using such a method. The results indicate that the OECS model can yield solution in an efficient way, whereas the MECS model should be used if solutions of greater accuracy are desired.

The differential equation for inclined cables under axial narrow-band stochastic excitations is established with consideration of the cable sag and variations of cable tension along the cable. Gaussian and first-order non-Gaussian closed-form solutions are derived by employing the statistical moment truncation method to solve the moment equation. A long cable (Cable A20 of No. 2 Nanjing Bridge over the Yangtze River) is taken as an example to demonstrate the application of the theoretical model presented. The Monte Carlo method is also adopted to simulate the responses of the cable numerically under investigation. The general response characteristics of the cable are analyzed, particularly, the variation characteristics of the response of the cable depending on the excitation bandwidth when the ratio of the central frequency of excitation to the first frequency of cable is equal to one or two. Parametric vibrations of the real Cable A20 excited by the buffeting vibration of the bridge deck of No. 2 Nanjing Bridge over the Yangtze River are also calculated.

The dynamic behavior of stay cables has a significant impact on the safety and serviceability of cable-stayed bridges. As tuning such dynamic behavior could be effectively achieved by a damping increase on stay cables, this paper investigates on the feasibility of increasing damping on two stay cables simultaneously through interconnecting them with a negative stiffness damper (NSD). It presents the passive realization of the NSD through the following process. First, under harmonic excitations, the steady-state dynamic responses of the two cables in the network are derived. Then, the asymptotic solutions for the additional modal damping ratios are formulated with the critical viscous damping and negative stiffness determined approximately. Subsequently, a parametric analysis is performed to verify the theoretical derivations using two stay cables of a real long-span cable-stayed bridge, under a series of numerical evaluations consisting of sinusoidal excitations and white noises vibrational responses for both cables. Both the theoretical and numerical results show superior damping enhancement by the NSD, in that the vibration responses of the two cables are reduced remarkably.

The nonlinear energy sink (NES) has been verified to have a broadband damping effect in many studies. In this paper, the in-plane vibration of an inclined cable attached with an NES is considered. First, nonlinear motion equation of the cable under an axial harmonic excitation (parametric excitation) is derived on the basis of Hamilton’s principle. The ordinary differential equations (ODEs) of the system are derived by Galerkin method and solved by fourth-order Runge–Kutta method. In this way, the suppression effects of the NES on primary resonance, 1/2-order sub-harmonic resonance and second-order super-harmonic resonance of the cable are investigated when the cable is subjected to a parametric excitation. Then, by optimizing the parameters of the NES individually, the corresponding results are compared with those of the uncontrolled system and the cable with a tuned mass damper (TMD). Meanwhile, the robustness of the NES against changes in the amplitude of axial excitation is also studied. The results demonstrate the high-efficiency vibration suppression of the NES and the vibration suppression effect of the optimized NES on the cable shows better performance in terms of multi-modality compared with the optimized TMD.

The stability of the parametric resonance of a controlled stay cable with time delay is investigated. The in-plane nonlinear equations of motion are initially determined via the Hamilton principle. Then, utilizing the method of multiple scales, the modulation equations that govern the nonlinear dynamics are obtained. These equations are then utilized to investigate the effect of time delays on the amplitude and frequency-response behavior and, subsequently, on the stability of the parametric resonance of the controlled cable, that it is shown to depend on the excitation amplitude and the commensurability of the delayed-response frequency to the excitation frequency. The stability region of the parametric resonance is shifted, and the effects of control on the cable become worse by increasing time delay. The work plays a guiding role in the parametric design of the control system for stay cables.

The characteristics of low damping and closely spaced natural frequencies make stay cables susceptible to wind-induced vibrations. This work proposed a novel damping device consisting of tuned mass damper (TMD) and rigid cross-tie (RCT) to mitigate the vibration of stay cables effectively. Two adjacent stay cables interconnected with RCTs can provide installation locations for TMDs, thus making the novel TMD-RCT control system feasible. Experimental control tests were carried out on a two-cable model of adjacent stay cables built in laboratory, where one TMD was designed based on the fundamental vibration mode of the stay cable. The effects of CT stiffness, number of RCTs, mass ratio, and installation position on the vibration reduction effect of the device were studied. To validate the efficacy of the proposed TMD-RCT device in vibration mitigation of stay cables under different loading cases, simulation tests and corresponding control performance evaluation were conducted.

Installing mechanical dampers near the cable anchorage is a commonly used measure for suppressing rain-wind-induced vibrations (RWIVs) of stay cables. However, the high-mode vortex-induced vibrations (VIVs) are still observed on super-long stay cables installed with dampers. To this end, the study presents the combination of a negative stiffness damper (NSD) and Stockbridge dampers (SDs) to simultaneously suppress cable RWIVs and VIVs. In the proposed cable–NSD–SDs system, the NSD is installed near the cable anchorage to suppress cable RWIVs, and the SDs are installed at a higher location to suppress cable VIVs. First, the generalized characteristic equation of the cable–NSD–SDs system is derived for computing the coupled damping effect. Subsequently, a novel design method of an NSD and two SDs for mitigating cable multi-mode vibrations is proposed, and its effectiveness is numerically verified on an ultra-long stay cable of the Sutong Bridge. Finally, the control performance of an NSD and two SDs for the cable under white noise and harmonic excitations is emphatically evaluated and compared. Results indicate that the NSD–SDs system is quite effective for mitigating high-mode vibrations of super-long stay cables. Compared with the cable–NSD system, the cable acceleration response of the cable–NSD–SDs system is reduced by over 35%.