# Flow-Induced Vibration of Cantilever Type Elastic Material in Straight Tricylinder
## 3 Results and Discussion
### Streamline Field  
Based on the observations from Figures 5 and 7a, it can be inferred that the wake of the upstream cylinder has an approximate influence range of 2 D along the Z-axis. In Figure 7b, it is evident that for L/D = 3 and L/D = 4, the wake exhibits a highly disordered pattern, indicating its impact on the downstream cylinder's wake. For L/D = 5 and L/D = 6, vortices are still discernible; however, some flow lines remain relatively straight and unaffected by vortices. The vortex from upstream and downstream mixed to produce a bigger scale vortex, which indicates that the upstream cylinder wake has a continuous influence on the downstream cylinder wake. When L/D = 7, there is a significant reduction in vortex activity within the wake region; numerous flow lines align closely with straight trajectories, while only minimal mixing occurs between vortices generated by both cylinders. Notably absent are any large-scale vortices affecting all three cylinders simultaneously, thus  
Figure 6: Vorticity diagram with L/D = 3\(-\)7 and H/D = 7.5\(-\)30.  
indicating a sharp decrease in the influence exerted by an open wake originating from an upstream source.  
It is evident in Figure 7 that the longitudinal vorticity primarily is concentrated in the middle and lower regions. Combining with the vorticity shown in Figure 6 further reveals that the intensity of vorticity is higher near H/D = 15 and H/D = 22.5 in the middle region. The development of eddy currents at H/D = 30 on top is predominantly horizontal due to its location above the cylinder's top. As a result, it remains relatively unaffected by the upstream cylinder, leading to a stable flow with reduced Y\(-\)axis direction vorticity and dominance in the horizontal direction. In the area near the middle of the column, the influence of the upstream column is greater so that the vorticity formed by it changes obviously in the vertical direction. With an increase in spacing ratio L/D, the wake tends to flatten both horizontally and vertically.  
The Z-axis flow velocity diagram of different cylinders along the X-axis section when D/L = 6 is presented in Figure 8. The Z-axis flow diagram allows for a quick visualization of the distribution of the flexible cylinder in the Y\(-\)axis vortex. For instance, when H/D = 7.5, numerous regions with opposite flow directions can be observed near cylinder 1 in Figure 8a, indicating the formation of vortices and indirectly reflecting their intensity. In Figure 8a, concentrated regions opposing the flow direction can be seen around H/D = 7.5, with lengths reaching up to 10 D, suggesting significant vorticity in these areas. In Figure 8b, parts within the same region exhibiting opposite flow directions appear more dispersed, indicating lower vorticity levels here compared to Figure 8a. In Figure 8c, parts within the same region displaying opposite flow directions are concentrated; however, the length of this region is only 5 D, implying smaller vorticity than that observed in Figure 8a but larger than that in Figure 8b. From Figure 5, it can be observed that at this point in time, wake streams from cylinder 1 and cylinder 2 as well as from cylinder 3 mutually influence each other; furthermore, when H/D = 7.5, it is evident that there is relatively high vortex intensity associated with cylinder 3, while relatively low vortex intensity corresponds to cylinder 2 at this point in time, which supports this conclusion.