## 4 Results and Discussion
### Excitation Force Coefficient Characteristics  
The excitation coefficient and the RMS values of displacement of the riser model in the CF direction at the velocity of 1.6 m/s were obtained by using the vortex-induced force coefficient identification method, as shown in Figure 11.  
Figure 10: (a) F01 and F02. (b) F03 and F04. Total mass distribution of CF and IL sections along pipe length at 1.6 m/s flow rate for the four types of riser (m\({}_{\text{s}}\) is the structural mass per length of pipe model; m\({}_{\text{a}}\) is the added mass per length of pipe model; A/Douyancy is the ratio of VIV displacement amplitude to outer diameter of buoyancy module;\(f_{\text{F01,CF}}\),\(f_{\text{F02,CF}}\),\(f_{\text{F03,CF}}\) and \(f_{\text{F04,CF}}\) are the dominant VIV frequency of F01, F02, F03 and F04 in CF direction; V\({}_{\text{F01,CF}}\), V\({}_{\text{F02,CF}}\), V\({}_{\text{F03,CF}}\) and V\({}_{\text{F04,CF}}\) are the reduced velocity referring to \(f_{\text{F01,CF}}\),\(f_{\text{F02,CF}}\),\(f_{\text{F03,CF}}\) and \(f_{\text{F04,CF}}\)). Figure 11a,b show the distribution of the excitation coefficient and the RMS value of displacement of the pipe model in the CF direction before and after the installation of helical strikes with 25% coverage of the buoyancy modules. It can be seen that after adding helical strikes, the distribution of the excitation coefficient in the CF direction along pipe length is essentially the same as that without helical strikes, and it only changes from the positive excitation region to the damping region near the ends. However, the excitation force coefficients in the CF direction are reduced after covering helical strikes, and the variation range of the excitation coefficients is reduced from [\(-\)0.25, 0.23] to [\(-\)0.039, 0.035]. The main reason for this change may be that the vortex-shedding frequency of buoyancy modules increases after covering helical strikes, resulting in a change in its corresponding reduced velocity, which is around 6. In the force coefficient library obtained from the forced oscillation of the previous rigid cylinder [1], it can be seen that in the reduced velocity excitation range (5 to 8), the change in the reduced velocity has a great impact on the VIV force coefficient; especially near the reduced velocity of 6, the coefficient changes greatly. Figure 11c,d show the distribution of the excitation coefficient and the RMS value of displacement of the pipe model in the CF direction before and after the installation of helical strikes with 50% coverage of the buoyancy modules. When buoyancy modules are 50% non-uniformly covered, the buoyancy modules are densely covered near the left side (from 0 m to 3.005 m). It can be seen from the figure that the excitation coefficients of this section are all positive without helical strikes, which is in the excitation area. Moreover, due to the effect of buoyancy modules, the bare pipe section in the CF direction which is close to part of the densely covered section (Figure 11c) is also in the excitation area. After adding helical strikes, the excitation area on the riser decreases and the damping area increases, and the main changes occur in the densely arranged section of buoyancy modules and the adjacent bare pipe with helical strikes (the black solid line frame in Figure 11c). The excitation coefficient of the part covered by the buoyancy module in this pipe section decreases, and the excitation coefficient of the bare pipe with helical strikes (the dotted line box in Figure 11c) changes from positive excitation to negative excitation. This change is mainly due to the installation of helical strikes in the bare pipe, which weakens the vortex strength and even causes no symmetrical and stable vortices to be generated in the wake field, and the fluid acts as a damping effect on the riser.