# Flow-Induced Vibration of Cantilever Type Elastic Material in Straight Tricylinder
## 3 Results and Discussion
### Amplitude  
For a slender and flexible cylinder, it has been observed that the response dynamics of VIV exhibit chaotic and complex behavior, characterized by non-repeatable motions [4]. Consequently, unlike a rigid cylinder, the vibration of a flexible cylinder does not display obvious periodic changes. However, it does exhibit distinct fluctuation intervals which can provide insights into its movement trends. Figure 9 illustrates the Z-axis vibration curve of three cylinders with an L/D ratio of 3 and an H/D ratio of 30. The Z-axis  
Figure 7: Main view (**a**) and right view (**b**) of a flow chart with L/D = 3\(-\)7. The purple bead flow line originates from the cylinder, and the green streamer flow line passes between the cylinders.  
vibration of the three cylinders tends to remain generally stable within an amplitude interval of approximately 0.1 D. In particular, for the upstream cylinder 1, its Z-axis motion is symmetric along Z = 0; whereas for cylinder 2, under the influence of flow field effects, its motion path inclines towards the positive direction on the Z-axis with a deviation around 0.3 D. On the other hand, inflow from cylinder 3 causes its motion trajectory to deviate in the negative direction on the Z-axis with an approximate deviation magnitude also at about \(-0.3\) D. Overall, both cylinders' deviation trajectories are symmetrical along Z = 0.  
The deformation of flexible cylinder A at an L/D ratio of 3 and an H/D ratio of 30 is illustrated in Figure 10. In the figure, cylinder 2 and cylinder 3 indicate that the upstream cylinder 1 exhibits flexibility in the flow field. Cylinder 2* and cylinder 3* denote that in the flow field, the upstream cylinder 1 is rigid. The simulation results demonstrate that, in comparison with the rigid cylinder, the upstream flexible cylinder exhibits an overall decrease of approximately 0.02 D in terms of downstream stream-induced vibration amplitude A. Moreover, the amplitude range of cylinder 2 and cylinder 3 is roughly 0.01 D smaller than that of cylinder 2* and cylinder 3*. Regardless of whether it is cylinder 2, cylinder 3, or their counterparts denoted as cylinders 2* and 3*, all exhibit maximum amplitudes exceeding 1 D. Considering a spacing ratio L/D = 2 may lead to collision risks; hence, this study commences from a spacing ratio L/D = 3.  
The variation in amplitude A of L/D with different spacing ratios at an H/D ratio of 30 is illustrated in Figure 11. It can be observed from the figure that, within the range of the L/D ratio between 3 and 6, both the average values of amplitude A/D and the amplitude interval increase as the spacing ratio L/D increases. The maximum occurs at L/D = 6, where the maximum amplitude A/D reaches 1.23, and the amplitude interval reaches 0.1 D. When L/D exceeds 7, although the average relative amplitude A/D approaches it, with a spacing ratio of L/D = 3 exists a larger fluctuation interval of 0.1 D compared to when L/D = 3. By combining Figures 9-11 together, it can be concluded that the interference  
Figure 8: Flow through the center of the cylinder, Ut/D = 3000, Velocity diagram in the Z-axis direction: **(a)** cylinder 1, **(b)** cylinder 2, and **(c)** cylinder 3.  
Figure 9: The Z-axis vibration curve of the cylinder with L/D ratio of 3 and H/D ratio of 30.  
between the cylinders with a spacing ratio of L/D = 7 has been significantly reduced, and the flow-induced vibration expansion phenomenon has disappeared.