# Effects of the Configuration of Trailing Edge on the Flutter of an Elongated Bluff Body
## 3 Results and Discussions
### Discussion of Effect of TE  
Figures 21 and 22 show the variation of deck vibration amplitude with wind speed. In order to clearly reflect the vibration characteristics of the bridge deck in each case, the amplitude of the non-divergent vibration is calculated using the average amplitude within 30 s, and the amplitude of the hard flutter is expressed by the maximum amplitude during the vibration process. The flutter stability of the bridge deck increases with the increase in the \(\beta\) except in case 30c-45. Similar to the torsional amplitude, except in case 30c-45, the critical flutter wind speed on the vertical degree of freedom increases gradually with the increase in the angle of the TE \(\beta\).  
Next, this paper compares and analyzes the critical wind speed when the bridge deck starts to vibrate \(U_{s}\), the LCF wind speed range \(V_{L}\), and the critical wind speed of the hard flutter vibration \(U_{f}\). Figure 23 shows curves of \(U_{s}\), \(V_{L}\), and \(U_{f}\) followed by the change in \(\beta\). Among them, \(U_{s}\) gradually increases with the gradual increase in \(\beta\) while the curve of \(V_{L}\) and \(U_{f}\) changing with \(\beta\) drops at \(\beta=45^{\circ}\), and then gradually increase as \(\beta\) increases.  
Figure 21: Torsional amplitude changes with \(U_{r}\).  
Figure 20: The phase difference between torsional vibration and vertical vibration at various apex angles of the trailing edge.  
It shows that when \(\beta>45^{\circ}\), the increase in \(\beta\) has a significant inhibitory effect on flutter, which means the more blunt the TE of the bridge deck, the stronger the flutter stability. In this paper, the value of \(\cot(\beta)\) is used to describe the streamline performance of the TE. Figure 24 shows the change of streamline performance with \(\beta\). It can be seen that the absolute value of the slope of the curve gradually decreases with the increase in the \(\beta\). That means the decreasing speed of streamline performance of the TE gradually decreases, which is basically consistent with curves in Figure 23 when \(\beta\
eq 45^{\circ}\). The streamline performance of the TE has obvious correlation with the flutter characteristics and flutter stability of the bridge deck, while the streamline performance of the TE has a direct impact on the vortex in the wake region. The poorer the streamline performance of the TE is, the more complicated the distribution and movement of the vortex structure in the wake area will be, which means the distribution and motion law of the vortex in the wake area have an important influence on the flutter characteristics and flutter stability of the bridge deck.  
As for 30c-45 (\(\beta=45^{\circ}\)), the flutter characteristics of the model are quite different from other conditions. First, during the process of fluttering, there is basically no vibration in the vertical degree of freedom, which indicates until hard flutter develops, the vertical and torsional vibrations of the model are still not completely coupled. Secondly, when \(\beta\geq 30^{\circ}\), as \(\beta\) increases, \(U_{f}(\beta\
eq 45^{\circ})\) will gradually increase and \(V_{L}(\beta\
eq 45^{\circ})\) will gradually decrease, while \(U_{f}(\beta=45^{\circ})<U_{f}(\beta=30^{\circ})\) and \(V_{L}(\beta=45^{\circ})<V_{L}(\beta=60^{\circ})\). The specific reasons need to be further experimentally studied.