## 5 Cause and Mechanism of the Intense Vibration of the 3# Surface Outlet Gate
The amplitude coefficient curves in cases 6, 7 and 8 are also shown in Figure 20.  
It is noted that the red vertical line in Figure 20 represents the ratio between the actual external excitation frequency and primary structure frequency, and thus the longitudinal coordinates of the interaction points between the red vertical line and the other four frequency response curves denote the amplification factors of the dynamic response of the 3# surface outlet gate in the actual vibration. The variation law for the vibration amplification factors calculated from the proposed theoretical model in different cases is in accordance with the results of the prototype test results, which indicates that the proposed clarification and theoretical model is reasonable and accurate. The intense vibration of the surface outlet gate has caused concerns about the operational safety of this hydraulic gate. According to the prototype test, the gate vibration far exceeds the safety threshold under adverse working conditions, which directly led to the change of the gate operation mode. In the discharge process of recent years, the surface outlet gates are always opened first and the gate opening gradually increases with increasing discharge until the gate bottom is separated from the water surface. Then, the mid-level orifices begin to be put into operation. Based on the current gate opening mode, the vibration problem is not completely solved because a relatively large vibration of the surface outlet gate will still be generated when the surface outlet gate and the mid-level outlet gate are opened simultaneously. Due to the limited inflow volume of the reservoir and the flow volume used to generate electricity, the surface and mid-level orifices will be simultaneously operated only when the discharge volume is very large, and the operation time of this adverse working condition is significantly reduced. After several years of operation, the surface outlet gate has not yet been damaged, but the vibration problem is a threat to the hydraulic gate safety in the case of long-term operation under the general working conditions and short-term operation under working conditions with a large discharge. Based on the research presented in this article, it is a feasible to make the natural frequency of the surface outlet hydraulic gate very different from the dominant frequency of the actual vibration by applying the theory of structural modification. Alternatively, the discharge conditions of the mid-level outlet can be improved to significantly reduce the flow-induced vibration of the mid-level outlet  
Figure 20: Frequency response of 3# surface orifice gate in different cases: (**a**) the entire graph; (**b**) partial enlarged graph. gate so that the external excitation acting on the surface outlet gate will be attenuated. The detailed and complete approach for vibration reduction will be further studied in the subsequent research. It is necessary to point out that due to the complexity of the practical problem, the theoretical model proposed in this paper is significantly simplified, which is acceptable for the qualitative clarification of the cause and mechanism of the hydraulic gate vibration amplification. In order to calculate the structural dynamic response more accurately and in greater detail, the influence of fluid-solid coupling parameters on the gate vibration amplification effect, the mutual influence among accessory structures and the cross correlation between different vibration modes also need to be further investigated.