## 5 Aeolian Vibration and Its Controlling
### Result  
As described above, the analysis of bending strains of an individual conductor (fixed at both ends) and conductor and cable within the long-span CRS are shown in Figure 24. For the case of the long-span CRS, it is worth noting that its dynamic bending strain of conductor had significant change trends between the individual conductor. The bending strain of the conductor of the CRS increased with frequency in the low-frequency stage and decreased after a peak value, where the frequency was about 7.5 Hz. The reasons for this phenomenon were the source of increasing equivalent lift force and dissipating the power of the conductor with frequency. The equivalent lift force led to an increase in vibration, but dissipating power of the conductor suppressed it. Additionally, the structure feature of CRS limited the effect dissipating the power of the conductor, especially in the low-frequency stage. On the other hand, when VIV occurs in cable, the bending strain approximately increases with frequency except for a peak value of 4 Hz. It was concluded that compared with conductor conventional tower-line system, long-span CRS was more vulnerable because of the larger amplitude of VIV. Conductor and suspension cables were modeled independently and studied individually. The results of VIV occurred in different parts of long-span CRS were studied. In Figure 25, the distinction between VIV occurred only in the conductor or the cables, and amplitude changes after the damper was installed were shown. Dampers have a limited effect in the low-frequency stage for conductors but a significant effect in almost all frequency stages for suspension cables. Moreover, dampers can effectively clip the peak of amplitude besides reducing the amplitudes of the suspension cable. Figure 26 considered that VIV occurred in both the conductor and suspension cable. Compared with Figure 25, the significant difference is that VIV occurred in cable leads to a faster increase in amplitudes of the conductor in 3-6 Hz but has no effect on the peak amplitude. However, with the increase in frequency, which leads to the dissipating power of the damper increasing, amplitudes of the conductor were significantly reduced. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Substructures** & **Big Damper Mass** & **Small Damper Mass** \\ \hline Mass of damper (kg) & 2.557 & 1.842 \\ Length of damper cable (m) & 0.202 & 0.145 \\ Center of mass to the junction (m) & \(3.25\times 10^{-2}\) & \(1.21\times 10^{-2}\) \\ Rotary inertia (kg\(\cdot\)m\({}^{2}\)) & \(6.51\times 10^{-3}\) & \(3.30\times 10^{-3}\) \\ Flexural rigidity of damper cable (N\(\cdot\)m\({}^{2}\)) & 22.41 & 22.41 \\ Damping ratio of the system [29] & 0.16 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Structure parameters of FRSD. Figure 23: Detail of FE model of FRSD damper. Figure 24: Bending strains of conductor and cable in 89 mm from clamp exit (wind load applied on conductor and cable). Figure 25: Amplitudes of long-span CRS (VIV occurs separately in conductor or cable). Figure 26: Amplitudes of long-span CRS (VIV occurs both in conductor and cable). In summary, the installation of dampers had an effect on the vibration characteristics of a long-span CRS. Additionally, dampers in the conductor and suspension cables significantly reduce amplitudes, and the effect increases with frequency. Accordingly, the installation of dampers on both conductor and suspension cables was effective and essential to protect the structure from the danger of VIV. The above discussion provided the preliminary basis for the design of protective measures of long-span CRS. Attaching dampers to the conductor and suspension cable was a practical protective measurement regarding VIV of long-span CRS. For suspension cables, the maximum amplitude occurred in a lower frequency band, which needs more attention. For the conductor, the resonance frequency band of the conductor and suspension cable should be of concern because of the larger dynamic bending strain.