## 4 Results and Discussion
### The Added Mass and Its Coefficient Characteristics  
Based on the above displacement response results, the added mass coefficient at each section of the riser was further calculated and identified, as shown in Figure 9. It shows that:  
Figure 8: The RMS values of displacement under vortex-shedding frequency of buoyancy modules (uniform flow 1.6 m/s). Figure 7: Axial distribution of RMS value of VIV displacement under uniform flow (1.6 m/s). (1) After buoyancy modules are covered, the added mass coefficients on buoyancy modules are much smaller than on the bare pipe. The added mass coefficient on the flexibleiser with buoyancy modules has a \"sawtooth\" distribution along the pipe. The maximum added mass coefficient on the bare pipe is 10.0, and the added mass coefficient on the buoyancy modules even appears negative. This phenomenon may be due to the effect of fluid viscosity when VIV occurs and the outer diameter of the buoyancy module is much larger than that of the bare pipe, which leads to more added water attached to the part closer to the buoyancy module. When the adjacent buoyancy modules are closer and closer, there will be more and more added water. When the bare pipe's outer diameter is used to calculate the added mass coefficient of the added water, the coefficient will be much larger than that of the bare pipe. The specific reasons can be further analyzed by fine simulation methods such as CFD. (2) The helical strikes coverage has little effect on the added mass coefficient of the buoyancy modules and the bare pipe section. For the pipe with buoyancy coverage of 25%, the average added mass coefficient in both directions before and after the helical strikes coverage has little change. Before and after the helical strikes are covered, the average added mass coefficients on the bare pipe section in the CF direction are 3.66 and 3.77, respectively, and the average added mass coefficients of the buoyancy module section are \(-\)0.33 and \(-\)0.26, respectively. For the riser with an uneven buoyancy coverage of 50%, the average added mass coefficient of the densely covered part of buoyancy modules (0-3.005 m) changes from 3.72 to 3.62 after the helical strikes are covered. The average added mass coefficient of the sparsely covered part of buoyancy modules (3.005-7.9 m)  
Figure 9: (a) Added mass coefficients and A/D for F01 and F02. (b) Velocity and acceleration of F01 and F02. (c) Added mass coefficients and A/D for F03 and F04. (d) Velocity and acceleration of F03 and F04. Added mass coefficient distribution under uniform flow with velocity of 1.6 m/s (Ca CF: added mass coefficient in CF direction; A/D\({}_{\text{bouyancy}}\) 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 frequencies of F01, F02, F03 and F04 in CF direction; \(\text{V}_{\text{F01,CF}}\), \(\text{V}_{\text{F02,CF}}\), \(\text{V}_{\text{F03,CF}}\) and \(\text{V}_{\text{F04,CF}}\) are the reduced velocities referring to \(f_{\text{F01,CF}}\), \(f_{\text{F02,CF}}\), \(f_{\text{F03,CF}}\) and \(f_{\text{F04,CF}}\)). remains at 0.02. This phenomenon shows that the added mass coefficient of the helical strikes can be approximated by the coefficient of bare pipe when predicting the VIV of covering buoyancy modules and helical strakes. According to the above analysis, the added mass coefficient of the buoyancy modules is still much smaller than that of the bare pipe after covering helical strakes and generally presents a \"sawtooth\" distribution. Further calculation of the total mass at each section of the riser (Figure 10) shows that the distribution of the total mass (structural mass plus added mass) along the length of the pipe of the buoyancy modules and bare pipe after covering helical strakes is similar to the riser without strakes, showing an overall continuous distribution, and the total mass varies less in the half-wavelength except near the displacement stagnation point.