# Analysis of Wind-Induced Vibration Response of Transmission Wire Under Crosswind in Canyon Terrain
## 6 Wind Vibration Characteristics of Wire Under Step Wind Speed Input
### Influence of Different Step Amplitudes  
The wind speed change diagram, the lateral force change diagram of the wire, and the time-history curves of the z-displacement and y-displacement of the midpoint of the wire under conditions 1, 2, 3, and 4 are shown in Figure 13. Different conditions are expressed in terms of their accelerations. In the figure legend, the acceleration is shown as \"A\". The figure shows that the change trend of the z-direction displacement of the wire was closely related to the lateral force on the wire. Both figures show the wire underwent attenuation oscillation after the wind speed reached stability and eventually reached a stable value. The z-displacement of the wire was analyzed as the step response in the control system. The oscillation attenuation process of the wire was similar to the underdamped step response process of a typical second-order system, with a damping ratio of 0 < \(\zeta\) < 1. The time domain performance indicators of the control system, calculated from the resulting data for each condition, are shown in Table 4. In the control system, _tp_ is the peak time, and c(_tp_) is the maximum deviation.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Condition**} & **Peak Time** & **Maximum Deviation** & \multirow{2}{*}{**Overshoot**} \\  & _tp_ (s)** & **c(_tp_) (mm)** & \\ \hline
1 & 1.65 & 72.41 & 41.2\% \\
2 & 1.66 & 126.31 & 36.3\% \\
3 & 1.65 & 191.75 & 35.7\% \\
4 & 1.64 & 267.7 & 36.8\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Time domain performance index of each condition (z-direction).  
Figure 12: Pressure around the wire.  
Figure 13: Time–history curves of wind speed, lateral force, and displacement.  
Figure 14 shows the curve of the maximum deviation with the wind speed and the fitted linear trend line. The figure shows that the maximum deviation in the z-direction presented a linear change with the increase in the wind speed. The change equation is  
\[y=13.026x-128.55 \tag{8}\]  
where \(y\) is the maximum deviation, and \(x\) is the wind speed.  
Based on the z-direction displacement of the wire, the time required for the wire under each working condition to reach a \(\pm\)5% error of oscillation within the steady-state value could be obtained, where the adjustment time ts (\(\Delta\) = 0.05) was successively 6.1 s, 6.4 s, 6 s, and 6.3 s, and the average value was 6.2 s. The variance value of each datum was 0.025, and the degree of data dispersion was small. Therefore, this average value was suitable as the expected value of the adjustment time of each step condition. The peak time of the conductor displacement was close, the overshoot of the conductor displacement was approximately 38.5% (\(\pm\)3%), the oscillation adjustment time was similar, and the displacement oscillation trend was similar. The oscillation period was 1.75 s, 1.82 s, 1.77 s, and 1.74 s in turn, and the average value was 1.77 s. The variance value of each datum was 0.003, and the degree of data dispersion was small. Therefore, this average value was suitable for the expected value of the oscillation period of each step condition. Therefore, the wind vibration response of the wire was mainly determined by its own material characteristics.  
The y-displacement diagram of the wire shows that the oscillation amplitude of the conductor in the y-direction increased with the increases in the stable wind speed, and the y-direction oscillation amplitude was smaller than that in the z-direction under every condition.