## 2 Prototype Test for the Vibration of the Hydraulic Gate
### Vibration of the Mid-Level Outlet Radial Gate  
The mid-level outlet on the Jinping arch dam is equivalent to a short pressure pipe and the fluctuating pressure generated by the high-velocity discharge flow in the pressure pipe may mainly consist of high frequency components [35]. As shown in Figure 4, the test point placement on the mid-level outlet gate (No. 3#) was given and triaxial acceleration sensors were installed at each measuring point. Figure 4: Test point placement on 3# mid-level orifice gate. Figure 3: Arrangement of the surface and mid-level outlets on the arch dam body. Figure 2: Photos of prototype testing. (**a**) Sensor installation; (**b**) cable traction; (**c**) data acquisition. In Figure 5, the root mean squares (RMSs) and dominant frequencies of the acceleration histories measured at each test point on the mid-level gate (No. 3#) are illustrated. The unit gal, shown in Figure 5 and the following several other figures, is frequently used in earthquake engineering and can be expressed as 0.01 m/s\({}^{2}\) (i.e., 1 cm/s\({}^{2}\)) in the international system of units. It is noted that for the test points on the gate leaf, the x-direction represents the lateral direction of the gate leaf, which always remains horizontal, the y-direction represents the tangential direction of the gate leaf, and the z-direction denotes the radial direction of the gate leaf. Moreover, for the test points on the supporting arms and the concrete corbels, the x-direction denotes the lateral direction which always keeps horizontal, the y-direction represents the axial direction of the supporting arm, and the z-direction represents the direction which is perpendicular to the arm. Note that the aforementioned sensor directions are defined in the local coordinate systems and the directions in the global coordinate system may change with gate opening. As mentioned above, the triaxial sensor was installed at each measuring point, which meant that the vibrations in three mutually perpendicular directions in space could be measured at each measuring point but the directions of the sensors at different measuring points may have been different. Specifically, the directions of sensors installed on the concrete corbels did not change because the concrete corbel did not rotate when the gate opening changed. For the sensors installed on the gate, the x-direction (lateral direction) always remained horizontal and did not change in the global coordinate system; the y- and z-directions were dependent on the gate opening and were inconsistent under different working conditions. Figure 5 indicates that the vibration in the z-direction is more intense than the vibrations in the x- and y-directions, and, except in rare cases, the dominant frequencies of the acceleration histories measured at each test point are approximately 26.2 Hz. It is noted that only the 3# mid-level outlet gate is fully opened in case 1, so that the vibration is almost certainly induced by the fluctuating pressure generated from the high-velocity flow that is discharged through the 3# orifice. According to the test results, the amplitudes and dominant frequencies for the vibrations of the 2# and 4# mid-level orifice gates in case 2 are almost the same as those of the 3# mid-level orifice gate in case 1, which is probably because of the similar flow conditions. Generally, the dominant frequency of flow-induced pressure fluctuation ranges from 0 to 2 Hz and the high frequency vibration is unlikely to be caused. However, the fluctuating pressure generated by the high-velocity discharge flow may consist of high-frequency components [35], and the high-frequency vibration of the hydraulic gate occurs frequently in engineering practice [6; 36]. The detailed mechanism for the flow-induced vibration of hydraulic gates needs further investigation. Figure 5: RMSs and dominant frequencies of the acceleration histories measured on 3# mid-level orifice gate in case 1 (3# mid-level outlet gate is 100% opened and the corresponding discharge is approximately 1090 m\({}^{3}\)/s).