## 4 Results and Discussions
### Irregular Waves  
Similar to the calculation of the model under the regular wave, the time domain motions of the OC3 CM model under the irregular waves are also solved by the code. The results are discussed in the frequency domain obtained by transforming the time domain signal to the frequency domain through Fast Fourier Transform [40]. Figures 11-13 illustrate the frequency domain amplitude and the peak amplitude of the models at load cases 4, 5, and 6, respectively. Only the results in the low-frequency region are studied, which corresponds to the major contribution of the motion of the platform.  
From Figures 11a, 12a and 13a, it can be found that the first peak of the surge amplitude appears at around 0.01 Hz. In the frequency interval 0-0.04 Hz, the surge amplitude of the OC3 CM models is significantly smaller than the surge amplitude of the original OC3 model P0, and the surge amplitude  
Figure 10: The maximum and minimum values and average values of pitch motion from 600 s to 900 s for (**a**) case 1, (**b**) case 2, and (**c**) case 3.  
Figure 9: The maximum and minimum values and average values of heave motion from 600 s to 900 s for (**a**) case 1, (**b**) case 2, and (**c**) case 3.  
of the OC3 CM model P5 is found to be the smallest. Figures 11b, 12b and 13b show that the peak surge amplitude of the original OC3 model P0 is the largest, meanwhile, the peak surge amplitude of OC3 CM model P1 to P4 are almost the same, but those values are smaller than that of the original OC3 model P0. In load case 4, the peak surge amplitude of the original OC3 model P0 is 1.43 m, while the peak surge amplitude of OC3 CM model P5 is 0.88 m. This again illustrates that clump masses are more effective when they are mounted closer to the sea bed; in addition, it can be seen that the peak surge amplitude in the irregular wave situation can be reduced by about 38.4% by the OC3 CM model P5.  
Figure 11c, Figure 12c, and Figure 13c show that the first peak of the heave amplitude appears at around 0.01 Hz, and the amplitudes of the OC3 CM models coincide well with that of the original OC3 model P0 in the frequency interval 0-0.04 Hz. From Figures 11d, 12d and 13d, it can be found that the peak surge amplitudes of original OC3 model P0 and the OC3 CM models are staggered. However, those peak surge amplitudes are not very different from each other. In general, the OC3 CM models can reduce the peak heave amplitude by 10%-17% in an irregular wave situation.  
Figure 11: Frequency domain amplitude at load case 4 for (**a**) surge, (**c**) heave, and (**e**) pitch, and the peak amplitudes for (**b**) surge, (**d**) heave, and (**f**) pitch.  
As shown in Figure 11e, Figure 12e, and Figure 13e, the first peak of the pitch amplitude appears at around 0.01 Hz, which is the same as that of the surge and heave motions. Figure 11f, Figure 12f, and Figure 13f show that the peak pitch amplitude gradually reduces from the original OC3 model P0 to the OC3 CM model P5, even if the reduction is not obvious. Overall, the OC3 CM models can reduce the peak heave amplitude by 12%-19% in an irregular wave situation.  
In particular, the load cases have a significant impact on the motions of the model. By comparing Figure 11b, Figure 12b, and Figure 13b, it is evident that the higher the wave height, the larger the value of the surge. Similar conclusions can be drawn from other figures. In general, increasing the wave height and wind speed will make the value and amplitude of the motions of the OC3 model larger, as is expected.  
From the above analysis, the new model can be said to reduce the motions of the spar platform at an irregular wave. In particular, the peak amplitude of the surge is reduced by about 38.4%, while the  
Figure 12: Frequency domain amplitude at load case 5 for (**a**) surge, (**c**) heave, and (**e**) pitch, and the peak amplitudes for (**b**) surge, (**d**) heave, and (**f**) pitch.  
peak amplitude of heave and pitch are reduced by about 19% and 20%, respectively, by the OC3 CM model P5.