# Characteristics of Plane Gate Vibration and Holding Force in Closing Process by Experiments
## 3 Results and Discussion
### Characteristics of Holding Force
#### 3.2.1 Holding Force in Two Operation Modes  
From Equation (4), many factors can influence the holding force. In fixed gate opening, water column on the gate top and panel thrust have a relatively clear theoretical relationship with gate opening and upstream water depth. Thus, the characteristics of holding force mainly represent the characteristics of the pressure at gate bottom edge. Table 2 summarizes the holding force and its standard deviation in fixed gate opening. As upstream water depth increases, holding force generally decreases. In large gate opening, however, the holding force increases slightly with the upstream water depth increase because gate lattice is partly filled with water. The higher is the water level, the more water there is in the gate lattice and the greater is the holding force. In small gate opening, gate lattice is fully filled with water for different operation conditions. The influence of water in the gate lattice is insignificant for the holding force. In addition, standard deviation gradually decreases with the gate opening decrease for a certain upstream water depth, as shown in Table 2. Standard deviation is proportional to water depth in \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Opening Ratio \(e\)**} & \multicolumn{6}{c}{**Holding Force (kN)**} & \multicolumn{6}{c}{**Standard Deviation**} \\ \cline{2-9}  & **16 m** & **18 m** & **20 m** & **23 m** & **16 m** & **18 m** & **20 m** & **23 m** \\ \hline
0.8 & 2391.968 & 2437.359 & 2556.328 & 2513.437 & 0.182 & 0.216 & 0.289 & 0.346 \\
0.5 & 2324.772 & 2097.109 & 2008.719 & 1828.062 & 0.180 & 0.188 & 0.194 & 0.154 \\
0.3 & 2027.556 & 1781.109 & 1778.297 & 1114.462 & 0.176 & 0.174 & 0.139 & 0.132 \\
0.2 & 1864.470 & 1469.297 & 1517.547 & 678.750 & 0.162 & 0.134 & 0.137 & 0.126 \\
0.1 & 1371.220 & 721.812 & 104.765 & 477.906 & 0.133 & 0.130 & 0.132 & 0.124 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Holding force and its standard deviation in fixed gate opening. large gate opening. In small gate opening, it is inversely proportional to water depth. It indicates that upstream water depth impacts the pressure at gate bottom edge and the influence is nonlinear. Therefore, the suggestion that the pressure specified as 20 kN/m or a linear formula in the criterion does not seem to satisfy the practical requirements and need to further investigate [30]. For different upstream water depths, dominant frequency of holding force in each opening is 0.033-0.217 Hz. The frequency is not equal or close to the vertical vibration frequency and is not close to the flow pulsation frequency yet. Subsequently, Figure 7 plots the holding force for different conditions in closing process. As upstream water depth rises, the gate-closing time decreases gradually when gate stops moving. In the initial stage, holding force varies slightly and the maximum holding force occurs near 100 s. It indicates that vertical hydrodynamic loads varies significantly and can markedly change the holding force. In the transitional crawl stage, holding force decreases gradually in a reciprocation form. It is consistent with the existing research [31]. [PERSON] et al. [31] reckoned that holding force is a process of elastic energy stored by the steel cable releasing and storing. Specifically, the elastic energy of steel cable goes through a cycle of release-reserve-re-release-re-reserve in closing process. Afterwards, the friction forces by the loads acting on the gate body gradually increase, make the holding force gradually decrease and prevent the gate from dropping down. Figure 8a shows the fluctuation value of holding force in closing process. In the initial stage, the fluctuation value is small. As gate continues to go down, the fluctuation value suddenly increases rapidly. The higher is the upstream water level, the greater is the fluctuation value. Besides, Figure 8b depicts the dominant frequency of holding force. Frequency distribution is regular and its value reduces from 14 to 7 Hz in a step form.