## 1 Introduction
According to the prototype dynamic test results, a distinguishing feature of the vibration of the Jinping surface outlet gate from the vibration of hydraulic gates in other projects is that the vibration intensity decreases with the increasing opening of the gate. It is quite counterintuitive that the most intense vibration occurs when the surface gate is closed and, on the contrary, the vibration is reduced when the gate is opened and subjected to flow excitation. To the authors' knowledge, this vibration amplification effect of a closed hydraulic gate was first observed in the flood discharging process of the Jinping project and has not been reported in the existing literature. Obviously, this severe vibration is not affected by flow excitation, which prompts us to study the cause and mechanism of the vibration of the surface outlet gate from the perspective of structural dynamics. For the closed hydraulic gate, which is not subjected to flow excitation, its intense vibration is definitely caused by the vibration of the arch dam body, which is the only structure directly in contact with the gate. As the hydraulic gate is essentially an accessory structure installed on the mass concrete structure (i.e., the arch dam), it is natural to expect that the dynamic behavior of the hydraulic gate can be effectively described by developing the existing theory of dynamic vibration absorbers (DVA). The DVA theory is well-studied and considerable progress has been made since its first appearance in 1928 [18]. In the past several decades, different parameter optimization methods [19; 20] are presented and many improved types of DVA have been proposed, such as multi-degrees-of-freedom DVAs [21], multiple tuned-mass dampers [22], magnetoviscoelasticity dampers [23] and magnetorheologicaldampers [24]. Inspired by the theory of DVA, a simplified theoretical model in which the hydraulic gate is regarded as a DVA of the main structure (i.e., dam body) is established and then the cause and mechanism of the surface outlet gate vibration is clarified. As the theoretical analysis in this study is inspired by the DVA theory, the simplification that is frequently used in the analytical analysis in DVA theory is investigated. In the research on the reduction of vehicle-bridge coupled vibration using DVA [25; 26; 27], the actual structure is greatly simplified by regarding the bridge and vehicle as the simply supported beam and single mass block, respectively. In the analysis on the damping effect of the DVA on wind turbine vibration, simplified systems with a small number of degrees of freedom (DOFs), for example, three DOFs [28; 29] and five DOFs [30], are frequently applied to simulate the actual wind turbine. Moreover, complex structures with large numbers of DOFs are usually converted to single-degree-of-freedom (SDOF) structures by the mode decomposition method in many studies on structural vibration control [31; 32]. For theoretical research on the vibration reduction mechanism [33; 34], a two-DOF structure is the classical system that is frequently used to represent the structure-DVA system and is very convenient for further research. As the purpose of this paper is to clarify the cause and mechanism of the gate vibration and the calculation for the detailed structural dynamic response is not considered, we believe that this simplified two-DOF theoretical model proposed in this study is appropriate and the analysis results of this article are reasonable and effective. However, only the qualitative analysis results, including the clarification of gate vibration cause and mechanism and the rough estimate for the vibration amplification effect under different working conditions, are obtained, due to the limitation of this simplified theoretical model. The calculation model would be further improved to reasonably and precisely describe the actual conditions in the subsequent research in order to calculate the structural dynamic response more accurately and in greater detail.