## 3 Results and Discussion
### Vortex-Induced Vibration of the Risers
Figure 6: _Cont._  
From the test results, it is found that the amplitude of the response strain of the risers with the S-F end condition decrease to 1/10 of that of the risers with the S-S end condition. Figure 6a-c shows that the response strain of the Al riser is not obvious for all velocities. From Figure 6e-f, the response strain curve of the PMMA riser increases with increasing flow velocity; more specifically, 40 \(\mu\varepsilon\) for 0.2 m/s and 0.6 m/s and 70 \(\mu\varepsilon\) for 1.0 m/s. Similarly, the response strain curve of the UPVC riser increases with increasing flow velocity; from 30 \(\mu\varepsilon\) to around 120 \(\mu\varepsilon\). Figure 7 shows the response microstrain curves of the three risers at z = 0.5 m with a 65 N top tension force and the S-F end condition for flow velocities of 0.2 m/s 0.6 m/s and 1.0 m/s (experiment cases 10-12, 22-24, 34-36). Figure 6: Response microstrain curves of the three risers at z = 0.5 m with a 5 N top tension force and the S-F end condition. (**a**) 0.2 m/s, Al, case 4; (**b**) 0.6m/s, Al, case 5; (**c**) 1.0 m/s, Al, case 6; (**d**) 0.2 m/s, PMMA, case 16; (**e**) 0.6 m/s, PMMA, case 17; (**f**) 1.0 m/s, PMMA, case 18; (**g**) 0.2 m/s, UPVC, case 28; (**h**) 0.6 m/s, UPVC, case 29; (**i**) 1.0 m/s, UPVC, case 30. Figure 7: _Cont._  
Figure 7a-c shows that the response strain of the Al riser is not obvious for all velocities. From Figure 7e-f, the amplitudes of response strain for the PMMA riser are similar (40 \(\mu\epsilon\)) at velocities of 0.2 m/s and 0.6 m/s, and increase to 70 \(\mu\epsilon\) at velocities of 1.0 m/s. Similarly, the response strain curve of the UPVC riser increases with increasing flow velocity (Figure 7g-i); from about 40 \(\mu\epsilon\) (0.2 m/s and 0.6 m/s) to around 90 \(\mu\epsilon\) (1.0 m/s). From Figures 4-7, the VIV of Al risers is not obvious for all conditions, which indicates the significant effect of the modulus. It is also found that the amplitude of VIV with the S-F end condition is much smaller than that of VIV with the S-S end condition when the other parameters are the same. Generally speaking, the amplitude of VIV increases with increasing flow velocity, and the increment speed is much larger for risers with the S-S end condition. From the figures of the response microstrain of risers, it is obvious that the lock-in phenomenon does not happen for Al risers under all experiment cases. For the PMMA riser, the lock-in phenomenon occurs when the flow velocity reaches 0.6-1.0 m/s with the S-S/S-F end condition and 5 N top tension force. In terms of the UPVC riser, the beginning velocities that lead to the lock-in phenomenon are 0.6 m/s, 0.6-1.0 m/s and 1.0 m/s for 5 N with the S-S end condition, 5 N with S-F end condition, and 65 N with the S-F end condition, respectively. In addition, the possibility of a riser's \"lock-in\" could be evaluated by reduced velocity U\({}_{\rm r}\). Generally speaking, when U\({}_{\rm r}\) ranges from 4 to 8 [42], \"lock-in\" occurs. U\({}_{\rm r}\) can be calculated by U\({}_{\rm r}=\frac{\rm U}{\rm f_{\rm n}D}\), where U is the flow velocity, f\({}_{\rm n}\) is the natural frequency of the riser and D is the outside diameter of the riser. It is found that for experiment cases 14, 15, 18, 21, 24, 26, 29, 32, 35 and 36, the U\({}_{\rm r}\) are between 4 and 8. More specifically, the U\({}_{\rm r}\) are 4.8, 8.0, 6.2, 6.6, 5.3, 6.8, 5.0, 5.4, 4.6 and 7.7, respectively. Compared to the analysis using the microstrain amplitude of the risers directly, the conclusion gained from the U\({}_{\rm r}\) calculation (on the basis of the interrelationship between flow velocity and the natural frequency of the riser) is similar. We use the UPVC riser as an example, since the its vibration is the most significant in the test.