# Characteristics of Plane Gate Vibration and Holding Force in Closing Process by Experiments
## 3 Results and Discussion
### Characteristics of Vibration
#### 3.1.2 Vibration in Closing Process  
In closing process, this paper pays more attention to the gate vertical vibration. Figure 4 provides the vertical acceleration in closing process and its partial magnification diagram. Considering the characteristics of the vertical vibration, the gate vibration process can be divided into three stages: initial stage, transitional stage and crawl stage. In the initial stage, vibration acceleration is relatively small, and its regularity is insignificant. In the transitional stage, vibration acceleration increases gradually and gate continues to fall without intermittent motion. Subsequently, in the crawl stage, vibration acceleration increases continuously and gate drops down intermittently.  
Figure 5a shows the amplitude of vertical acceleration in closing process. The amplitude is different for different stages. In the initial stage, the amplitude varies slightly and maintains at 0.01 m/s\({}^{2}\). Afterwards, the amplitude increases gradually. The higher the upstream water depth, the greater the amplitude. The maximum amplitude can reach 0.11 m/s\({}^{2}\) approximately in the crawl stage and is almost 10 times higher than the initial stage. Moreover, Figure 5b plots the dominant frequency of the vertical vibration in closing process. For different upstream water depths, frequency distribution is relatively stable, and its regularity is remarkable after the initial stage. In this period, the dominant frequency gradually decreases from 14 to 7 Hz in the form of steps. As upstream water depth increases, the step moves into the origin of the coordinate and the frequency decreases gradually. This means gate vibration is directly related to the upstream water depth. Due to the dominant frequency far away from the flow pulsation frequency, we regard that gate vertical vibration is self-excited vibration in closing process.  
Figure 4: Vertical acceleration with gate-closing time: (**a**) vertical acceleration in closing process; and (**b**) partial magnification of vertical acceleration.  
In addition, Figure 6 reveals the amplitude of acceleration in lateral and horizontal direction. The characteristics of lateral vibration is the same as that of vertical vibration. Nevertheless, the vibration magnitude is relatively small, and the maximum of amplitude can reach 0.013 m/s\({}^{2}\). In horizontal direction, the amplitude changes a little with time and mostly maintains below 0.008 m/s\({}^{2}\). However, unusual fluctuation peaks of acceleration appeared near 130 s, as depicted in Figure 6a. The main reason for the situation lies in the defect of the model itself. Because the physical model was built in summer and fixed by steel structure, the guide track deformed slightly at a lower temperature. The defective area is located in large gate opening. Gate opening ratio \(\epsilon\) is roughly 0.83 and it is not the focus area of the study. Moreover, this defect does not significantly influence the vertical vibration results for a small gate opening, as described in Figure 5a. Therefore, we can ignore this defect in the following research.