# Chaotic Characteristic Analysis of Spillway Radial Gate Vibration under Discharge Excitation
## 3 SRG Analysis of the Prototype Test Data  
### Project Introduction  
A hydropower station on Yalong River is located in southwest China. There are five surface outlets in the spillway of the surface hole of the gravity dam section. Each outlet is equipped with an emersed radial gate with a radius of 21.00 m and width of 15.00 m. The material used for the SRG is Q345C steel. The SRG is arranged on the top of the WES weir, and the downstream is connected to the combination of a Y flaring gate pier, stepped spillway, and stilling basin to dissipate energy. Due to the large slope of the downstream channel of the gate, the flow pattern behind the gate is a typical free outflow, as shown in Figure 1. The working conditions of the dynamic prototype tests are detailed in Table 1.  
In order to fully track the vibration characteristics of the sensitive area (main beam and supporting arm) under hydrodynamic loads, three triaxial acceleration sensors were arranged on the top-left arm of the SRG (No. 3#) to measure the axial, vertical, and lateral vibrations of the supporting arm. Similarly, two triaxial acceleration sensors were arranged on the upper and lower main beams of the gate, and the schematic diagram of the measurement points is shown in Figure 2. The triaxial vibrati \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & **Absolute Opening** & **Gate Opening Ratio** & **Discharge** & **Velocity of Bottom** \\  & **Height h (m)** & \(e\) = _h/H_ (\%)** & **(m\({}^{3}\)/s)** & **Edge (m/s)** \\ \hline
1 & 3.50 & 18 & 606 & 15.78 \\
2 & 2.40 & 12 & 405 & 15.17 \\
3 & 1.00 & 5 & 183 & 16.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Three working conditions of the dynamic prototype tests. Figure 1: Flow pattern after the opening of the SRG (No. 3#). had a sensitivity of 1000 Mv/g with a frequency range of 0.1-2 KHz and a resolution of 0.00002 g. The sampling frequency and duration of each opening gate were 200 Hz and 120 s, respectively. It has to be emphasized that, for the three triaxial acceleration sensors on the gate leaf, the \(x\)-direction represented the radial direction of the gate leaf and the \(y\)- and \(z\)-directions denoted the tangential and lateral directions of the gate leaf, respectively. Moreover, for the sensors on the supporting arm, the \(x\)-direction denoted the axial direction of the supporting arm, the \(y\)-direction denoted the direction that was perpendicular to the supporting arm, and the \(z\)-direction represented the lateral direction. Note that the aforementioned sensor directions are defined in the local coordinate systems, and the directions in the global coordinate system may change with different gate opening values. For the sensors installed on the radial gate, the lateral direction (\(z\)-direction points on the gate leaf and supporting arm) always remained horizontal and did not change in the global coordinate system; the \(y\)- and \(z\)-directions were dependent on the gate opening heights and were inconsistent under different working conditions. Figure 3 shows the root mean square (RMS) of the vibration acceleration of the measuring points on the supporting arm under three working conditions. Point 5# is located at the front end of the upper-left supporting arm, close to the upper main beam on the gate; point 6# is located in the middle of the upper-left supporting arm; and point 7# is located at the back end of the upper-left supporting arm, which is close to the supporting hinge. In Figure 3, we can clearly observe that point 7 in the \(y\)-direction under condition 1 is the highest. The \(Y\)-direction denotes the direction that is perpendicular to the supporting arm. Firstly, according to the relevant prototype observation results, the vertical vibration of the supporting arm is obviously higher than that of the axial- and lateral-direction vibrations. Moreover, the position of point 7 is close to the end of the supporting arm, which is close to the joint of the fixed and movable supporting hinges.