## 2 Prototype Tests for the Spillway Guide Wall Vibration  
Three Gorges Hydropower Station (TGHS) is currently the largest hydropower station in the world, during the flood discharge, its structural safety is of utmost concern. The left spillway guide wall of TGHS is located between the left powerhouse and the spillway dam, as shown in Figure 1. During the flood discharge, the action area of fluctuation is large, and the action point is high, making the FIV a severe threat to the guide wall. To investigate the vibrational characteristics and mechanism of this guide wall, prototype tests of structural displacement were implemented. In the tests, several displacement sensors were installed on 1# spillway dam block and eight guide wall blocks (1#-8#). There are four measuring points on the dam block: 1# and 2# measuring points were located at the upstream side, 3# and 4# measuring points were located at the downstream side. Horizontal displacement sensors were arranged for each of the measuring points, and two vertical displacement sensors were arranged for 1# and 3# measuring points. Similarly, on each guide wall  
Figure 1: Hydraulic structures of the Three Gorges Hydropower Station (TGHS). (**a**) The layout of the TGHS project; (**b**) the enlarged view of left guide wall, spillway guide wall, and left powerhouse. block, the upstream measuring point 1# had one horizontal displacement sensor, and the downstream measuring point 2# had one horizontal displacement sensor and one vertical displacement sensor. All of the measuring points were tested simultaneously under the same working condition (listed in the Appendix A). The layout of the measuring points is illustrated in Figure 2. For the low dominant frequency of the vibration on the dam and the guide wall, the sampling frequency is 50 Hz. The signals of typical measuring points for vibration displacements on the 1# dam block and each of the guide wall blocks is processed by the Fourier Transform (FT). The FT spectrums of horizontal and vertical displacements of the 1# dam block and typical guide wall blocks are respectively shown in Figure 2. The layout of the measuring points, (**a**) The locations of measuring points; (**b**) dam block measuring points; (**c**) guide wall block measuring points (same layout for each block); (**d**) displacement sensor (horizontal and vertical); (**e**) acquisition devices. Figure 2: The layout of measuring points. (**a**) The locations of measuring points; (**b**) dam block measuring points; (**c**) guide wall block measuring points (same layout for each block); (**d**) displacement sensor (horizontal and vertical); (**e**) acquisition devices. and compared in Figures 3 and 4. For a better presentation and comparison of dominant frequencies, the power spectral densities (PSD) are normalized to 0-1 in the figures. From the FT spectrums, it can be observed that there are several similar dominant frequencies of horizontal displacements between the 1# dam block and the guide wall blocks in a broad range of 0-15 Hz. However, for vertical displacements, similar dominant frequencies are concentrated in a narrow range of 0-5 Hz, which is the range of the dominant frequency of flow excitation [5; 27]. For further investigation of this phenomenon, the dominant frequencies of horizontal displacements on the 1# dam block and guide wall blocks are listed in Table 1.  
As shown in Table 1, apart from the dominant frequencies of flow fluctuations (less than 5 Hz), some of the dominant frequencies of the horizontal displacements of guide wall blocks tend to match that of 1# dam block in an approximate range: the range of 5.58-5.81 tends to match 6.04; 7.14-7.22 tends to match 7.11; 16.26 tends to match 16.27. The vibrational components with frequencies higher than 5 Hz are considered to represent the structural resonances of certain modes under flow excitations because the fundamental frequencies of structures are usually higher than 5 Hz, which will be analyzed in detail in Section 4.2.