## 3 Results and Discussion
### Vortex-Induced Vibration of the Risers  
Generally speaking, the VIV responses of the riser in the flow direction and the cross-flow direction (90\({}^{\circ}\) with respect to the flow direction) are obviously different. In flow direction, the displacement is maintained at a relatively stable value, and vibrates slightly after the initial growth [35]. On the other hand, the vibration in the cross-flow direction of the riser is much more significant for the VIV study. It is noted that the cross-flow direction of the riser includes the separation and initiation of the wake and the shedding of vortices, and this fact significantly influences the initiation of the lock-in phenomenon. Moreover, the amplitude of vibration in the middle part of a riser is comparably lager than that at other locations. Therefore, the microstrain curves obtained from the strain gauges in the cross-flow direction (strain gauges 'c') at z = 0.5 m are utilized as a typical example presented in this paper. Figure 4 shows the response microstrain curve of the three risers at z = 0.5 m with a 5 N top tension force and the S-S end condition for flow velocities of 0.2 m/s 0.6 m/s and 1.0 m/s (experiment cases 1-3, 13-15, 25-27). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **S-S** & **S-F** \\ \hline Al & \begin{tabular}{c} 18.302 (T = 5 N) \\ 20.551 (T = 65 N) \\ \end{tabular} & \begin{tabular}{c} 22.019 (T = 5 N) \\ 25.7911 (T = 65 N) \\ \end{tabular} \\ \hline PMMA & \begin{tabular}{c} 6.251 (T = 5 N) \\ 7.582 (T = 65 N) \\ \end{tabular} & \begin{tabular}{c} 8.096 (T = 5 N) \\ 9.395 (T = 65 N) \\ \end{tabular} \\ \hline UPVC & \
\begin{tabular}{c} 4.429 (T = 5 N) \\ 5.521 (T = 65 N) \\ \end{tabular} &
\begin{tabular}{c} 6.006 (T = 5 N) \\ 6.456 (T = 65 N) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The natural vibration frequencies for different risers with different end conditions (Hz). Figure 3: Strain response under beating. Figure 4a-c shows that the response strain of the Al riser is not obvious for all velocities. From Figure 4e-f, the response strain curve of the PMMA riser increases with increasing flow velocity; more specifically, 20 \(\mu\varepsilon\) for 0.2 m/s, 150 \(\mu\varepsilon\) for 0.6 m/s, and 330 \(\mu\varepsilon\) for 1.0 m/s. Similarly, the response  
Figure 4: Response microstrain curves of the three risers at z = 0.5 m with 5 N top tension force and S-S end condition. **(a)** 0.2 m/s, Al, case 1; **(b)** 0.6 m/s, Al, case 2; **(c)** 1.0 m/s, Al, case 3; **(d)** 0.2 m/s, PMMA, case 13; **(e)** 0.6 m/s, PMMA, case 14; **(f)** 1.0 m/s, PMMA, case 15; **(g)** 0.2 m/s, UPVC, case 25; **(h)** 0.6 m/s, UPVC, case 26; **(i)** 1.0 m/s, UPVC, case 33.  
strain curve of the UPVC riser increases with increasing flow velocity; more specifically, 80 \(\mu\varepsilon\) for 0.2 m/s, 440 \(\mu\varepsilon\) for 0.6 m/s, and 1050 \(\mu\varepsilon\) for 1.0 m/s, from Figure 4g-i. Figure 5 shows the response microstrain curves of the three risers at z = 0.5 m with a 65 N top tension force and the S-S end condition for flow velocities of 0.2 m/s 0.6 m/s and 1.0 m/s (experiment cases 7-9, 19-21, 31-33). Figure 5: Response microstrain curves of the three risers at z = 0.5 m with 65 N top tension force and S–S end condition. **(a)** 0.2 m/s, Al, case 7; **(b)** 0.6 m/s, Al, case 8; **(c)** 1.0 m/s, Al, case 9; **(d)** 0.2 m/s, PMMA, case 19; **(e)** 0.6 m/s, PMMA, case 20; **(f)** 1.0 m/s, PMMA, case 21; **(g)** 0.2 m/s, UPVC, case 31; **(h)** 0.6 m/s, UPVC, case 32; **(i)** 1.0 m/s, UPVC, case 33. Comparing Figures 4 and 5, when the top tension force rises to 65 N from 5 N, the response strains of all three risers are not obvious, and the flow velocities have minor effects on them. Figure 6 shows the 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 for flow velocities of 0.2 m/s 0.6 m/s and 1.0 m/s (experiment cases 4-6, 16-18, 28-30).