Motion-Based Design of Passive Damping Systems to Reduce Wind-Induced Vibrations of Stay Cables under Uncertainty Conditions  
[PERSON]  
1 Department of Continuum Mechanics and Structural Analysis, Universidad de Sevilla, 41092 Seville, Spain; [EMAIL_ADDRESS] (J.N.-P.); [EMAIL_ADDRESS] (A.S.)  
2 Department of Continuum Mechanics and Theory of Structures, E.T.S. Ingenieros de Caminos, Canales y Puertos, Universidad Politecnica de Madrid, 28040 Madrid, Spain; [EMAIL_ADDRESS]  
3 Department of Structural and Geotechnical Engineering, Sapienza University of Rome, 00184 Rome, Italy; [EMAIL_ADDRESS]  
4 Correspondence: [EMAIL_ADDRESS]; Tel. : +34-910-674-1524  
The vibratory problems observed in cables of cable-stayed bridges may be classified in terms of the structural elements excited during the vibration phenomenon into the following [2]: (i) local-global vibratory problems, in which the vibrations involve the excitation of both the cables and the deck of the structure [4]; and (ii) local vibratory problems, in which only the cables of the structure are excited laterally [5]. These vibratory problems may be caused by either of the following: (i) direct excitation sources, such as road traffic, wind [6] or earthquake action [7], or (ii) indirect excitation sources, such as linear internal resonances, parametric excitations or dynamic bifurcations. In this paper, we focus on the case of wind-induced vibrations of stay cables, as this is the source problem of many vibratory issues reported in the literature [2]. As wind-induced vibrations can cause different structural problems on stay cables (like fatigue or comfort problems), two types of measures are normally adopted to mitigate the cable vibrations [8], consisting of either of the following: (i) modifying its natural frequency via the installation of a secondary net of cables [9]; or (ii) increasing its damping ratio via the installation of external control systems [2]. Such control systems for stay cables may be classified into three different groups [8]: (i) active [10]; (ii) semi-active [11]; and (iii) passive [12]. Active control systems for stay cables focus on controlling the dynamic response of the cable via the modification of its tensional state [13]. For this purpose, some kind of actuator, following the orders of a controller, acts on the cable in order to minimize the difference between the actual response of the cable (recorded by a sensor) and the allowable response value [14]. Although the theoretical research on the use of these devices has experienced a significant growth in recent years, their practical implementation in real cable-stayed bridges has been limited due to their high cost and the robustness problems associated with the power supply needed to guarantee their operation [2]. On the other hand, semi-active control systems focus on modifying the constitutive parameters of external damping devices deployed to control the response of the stay cable under external actions [15]. Among the different semi-active devices, magnetorheological dampers have been widely studied and implemented in real cable-stayed bridges [16]. Although semi-active damping devices outperform their passive damping counterparts [17] with a lower cost than active control systems, their efficiency is limited when they are employed under uncertainty conditions, since their performance highly depends on the control algorithm considered for the design [18]. Finally, passive control systems for stay cables focus on increasing the damping ratio of the cables via the installation of external devices, whose characteristic parameters are originally designed to mitigate the dynamic response of the structural system [19]. Due to the robustness of such passive damping devices [20], they have been installed successfully on numerous real cable-stayed bridges to reduce wind-induced vibrations [21].