## 1 Introduction  
In recent years, comprehensive hydraulic engineering projects with high dams and large reservoirs have been rapidly developing, especially in China, such as Three Gorges, Jinping, and Xiluodu. Simultaneously, flow-induced vibrations (FIV) of hydraulic structures, which frequently occur in these projects, have posed a significant threat to engineering safety [1]. To investigate the mechanism of the FIV, researchers have proposed several types of source and mechanism of the FIV. [PERSON] [2]classified the cause of the FIV as stable and unstable flow; according to the vibrational characteristics, [PERSON] [3] characterized the FIV as dynamic responses, self-controlled and self-excited vibrations, then demonstrated that changes in the structural geometry can eliminate the FIV; [PERSON] [1] categorized the sources of FIV excitation as extraneously-induced excitations, instability-induced excitations, and movement-induced excitations, then proposed that all the three types of excitation are simultaneously presented. Summarized from several current studies regarding the FIV of hydraulic structures, conclusions can be made that the FIV mechanism can be quite different for hydraulic structures with different scales and weights [4; 5]. For heavyweight structures, e.g., dams, spillways, plunge pool slabs, the effect of flow can be regarded as a simple load, and the vibrational response can be solved by regular dynamic equations. However, for lightweight structures, e.g., spillway guide walls, hydraulic gates, gate piers, the effect of flow cannot be simplified as a simple load, but an effect of the fluid-structure interaction (FSI), which can be equivalent to an added mass on the structure [6]. In other words, the structural vibration may absorb energy from the water. As a result, the vibration mechanism of lightweight structures is much more complicated than that of heavyweight structures. To give more definite illustrations for the vibration of lightweight structures, some new kinds of vibration mechanisms under FSI have been carried out to clarify some of the FIV phenomena in practice, with diverse theoretical models proposed. [PERSON] and [PERSON] [7] introduced a theory of self-exciting vertical vibration and demonstrated that self-excitation occurs in gates when suction forces are generated in the gate opening. [PERSON] and [PERSON] [8] claimed that the self-excitation of hydraulic gate vibration derives from the vortices, i.e., vortex-excited vibration, which can be attributed to the interaction between the elastic gate and the unstable shear layer underneath the gate. Meanwhile, under certain defined conditions, another type of vibration called galloping may occur [9], which is a phenomenon of self-excited large-amplitude oscillation and the energy of amplified vibration is absorbed from the fluid. Another new kind of vibration called beat vibration is detected on both the gate [10] and the guide wall [11], where the amplitude appears as a periodic change. Furthermore, by analyzing prototype tests, [PERSON] et al. [12] believe that the crest orifice gate vibration is induced and amplified by the mid-level orifice gate vibration when the natural frequency of the crest orifice gate is close to the frequency of flow excitation acting on the mid-level orifice. In hydraulic engineering projects with overflow gravity dams, e.g., Three Gorges, Xiangjiaba, spillway guide walls are built to separate the flow and stabilize the flow pattern. For the larger scale compared to other lightweight hydraulic structures (hydraulic gates and gate piers), the FIV damage of spillway guide walls can be more severe and harder to repair. There are many instances of damage reported, such as Texarkana, Trinity, Wan'an, and Wujiangdu [13]. It is concluded that the most common failure mode of the guide wall is fatigue crack. The guide wall structure is subject to various flow fluctuations for a long period, and the pressures between two sides of the guide wall are usually different.