# A Field Investigation on Vortex-Induced Vibrations of Stay Cables in a Cable-Stayed Bridge
## 3 Vibration Characteristics of Stay Cables and Wind Characteristics at the Bridge Site  
The vibration responses of selected stay cables were first studied. The data from three months (April, July, and August) in 2010 were collected to analyze the vibration characteristics of these stay cables. The statistical analysis for the vibration amplitudes in 10 min (10-min mean) was performed to observe the magnitude level of each stay cable. Because the vibration amplitudes of the stay cables were not steady with time, the root mean squares (RMSs) of 10 min acceleration time histories were employed to denote the vibration amplitudes, as shown in Figure 3. Two horizontal axes indicate the cable numbers and time, and the vertical axis denotes the RMS of acceleration, respectively. Figure 3: _Cont._  
Figure 2: Deploy of accelerometers at a cable. The anemometers are installed 6.0 m vertically above the deck’s surface. It is found that the stay cable CAC20 always has a larger amplitude than any other cables. The cable CAC20 has the same parameters as the cable CAC19. These two cables have a length of 323 m and a diameter of 0.12 m, resulting in an aspect ratio of 2692. The inclined angle is 26.3\({}^{\circ}\), and the angle between the cable plane and the longitudinal bridge axis is 2.59\({}^{\circ}\). The only difference is that one cable is at the upstream side, and the other cable is located at the downstream side. One damper was installed on each cable to control the wind-induced vibration. The ambient wind conditions, e.g., the mean wind speed, around the two cables should be close to each other; however, their vibration characteristics behave very differently. To determine the reason, an eye observation was performed to determine whether the damper was working. It was found that the connection between the damper with the cable CAC20 was loose and that the damper was not working well, which could be the reason why the cable CAC20 always has a larger amplitude for each month. After fastening the connection between the damper with the cable CAC20 from 2013, the larger amplitude vibration of the cable CAC20 was greatly suppressed by the damper, as shown in Figure 4. Therefore, the following analysis is mainly focused on the cable CAC20 in 2010 for the present study. Figure 3: Vibration response of stay cables of the stayed-cable bridge (10 min mean) in 2010. In the analysis of this study, the time histories of acceleration signals were numerically integrated in the frequency domain to obtain the corresponding time histories' displacements [15]. One record of time histories of acceleration and displacement for 12 h was shown in Figure 4(a), and the corresponding frequency spectrum of the acceleration history was shown in Figure 4(b). Whatever the acceleration and displacement, their amplitudes are not steady with time because the ambient wind conditions around the stayed cables are not uniform. As a long flexible stay cable of an actual cable-stayed bridge, high modal frequencies are the multiple of the fundamental natural frequency, which can be calculated as 0.378 Hz from Figure 4(b). It is found that the cable CAC20 has a multimode vibration with high frequencies. The vibration amplitude corresponding to each mode was shown in Figure 6. The larger vibration amplitudes are mainly located in the vibration mode range of 18 th to 40 th. Therefore, as a high-frequency vibration, the acceleration amplitude of the cable is large; however, the corresponding displacement amplitude is small. Figure 4: Vibration response of stay cables of the stayed-cable bridge (10 min mean) in 2013. Examining the vibration characteristics in the time and frequency domains cannot determine whether the vibration of the cable CAC20 is a VIV or other types of vibrations at present. Further investigation of the correlation between the vibration responses and wind characteristics will be performed to examine the vibration type and VIV mechanism of the cable CAC20. Figure 5: Vibration response of cable CAC20.