# Investigation on Ship Hydroelastic Vibrational Responses in Waves
## 4 Analysis of Numerical and Experimental Results
### Hydroelastic Responses in Irregular Waves
#### 4.4.3 \(M_{y}\) in Irregular Waves  
The time series of \(M_{BV}\)s amidships of the full-scale ship within 1100 s are shown in Figures 27 and 28, where the low-frequency components and high-frequency components are also separated from the total \(M_{BV}\)s by Fourier filtering similar to the treatment of \(M_{BV}\)s in regular wave conditions. Similar to the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Item**} & \multicolumn{3}{c}{**Condition 1 (V = 5 km, H\({}_{32}\) = 18.5 m,**} & \multicolumn{3}{c}{**Condition 2 (V = 18 km, H\({}_{32}\) = 9.185 m,**} \\  & & \multicolumn{3}{c}{**Tz = 12.5 s)**} & \multicolumn{3}{c}{**Tz = 11.5 s)**} \\ \cline{3-8}  & & **Experiment** & **Calculation** & **Error** & **Experiment** & **Calculation** & **Error** \\ \hline \multirow{4}{*}{Heave} & Peak significant value (m) & 3.59 & 4.03 & 12.26\% & 2.15 & 2.48 & 15.35\% \\ \cline{2-8}  & Trough significant value (m) & \(-3.67\) & \(-4.04\) & \(10.08\%\) & \(-2.22\) & \(-2.53\) & 13.96\% \\ \cline{2-8}  & Mean value (m) & \(-0.06\) & \(-0.025\) & \(---\) & 0.0082 & \(-0.037\) & \(---\) \\ \cline{2-8}  & Standard deviation (m) & 2.63 & 2.90 & 10.27\% & 1.56 & 1.75 & 12.18\% \\ \hline \multirow{4}{*}{Pitch} & Peak significant value (deg) & 4.75 & 5.27 & 10.95\% & 2.97 & 3.47 & 16.84\% \\ \cline{2-8}  & Trough significant value (deg) & \(-4.84\) & \(-5.32\) & \(9.92\%\) & \(-3.18\) & -3.51 & 10.38\% \\ \cline{1-1} \cline{2-8}  & Mean value (deg) & 0.025 & \(-0.00044\) & \(---\) & 0.0065 & 0.0003 & \(---\) \\ \cline{1-1} \cline{2-8}  & Standard deviation (deg) & 3.42 & 3.74 & 9.36\% & 2.20 & 2.49 & 13.18\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Statistical parameters of heave and pitch at CG of ship. Figure 26: Pitch responses in irregular wave condition 2. (**a**) Experimental result; (**b**) Numerical result. last section, here the experimental and numerical results are also qualitatively compared, and similar magnitudes and trends between calculation and measurement can be found from comparisons of \(M_{BV}\)s. As can be seen, several severe slamming events occurred during ship sailing in irregular waves because of high speed or large wave amplitudes. The slamming \(M_{BV}\)s decay rapidly due to the structural damping if two adjacent slamming events do not occur too closely. In irregular wave testing condition 1, the magnitude of slamming \(M_{BV}\)s is almost the same as that of low frequency \(M_{BV}\)s due to the large wave amplitude of irregular wave condition 1 on average. In comparison, for irregular wave testing condition 2, the magnitude of slamming \(M_{BV}\)s is obviously smaller than that of low frequency \(M_{BV}\)s due to the relatively smaller wave amplitude of irregular wave condition 2 compared with that of irregular wave condition 1. For these two irregular wave conditions, the experimental occurrence frequencies of wave impact manifested by the slamming \(M_{BV}\)s differ slightly, indicating that both large wave amplitude and high ship speed will increase the chance of slamming events. For the shown time series of these two irregular wave conditions, the numerical and experimental occurrence frequencies of wave slamming may differ from each other, since the numerical irregular waves are independently randomly generated. On average, the experimental and numerical time series of \(M_{BV}\)s show similar trends and magnitudes. Figure 27: \(Cont.\)  
Figure 27: Time history of \(M_{BV}\)s amidships in irregular wave condition 1. (**a**) Experimental result of total \(M_{BV}\); (**b**) Numerical result of total \(M_{BV}\); (**c**) Experimental result of low frequency \(M_{BV}\); (**d**) Numerical result of low frequency \(M_{BV}\); (**e**) Experimental result of high frequency \(M_{BV}\); (**f**) Numerical result of high frequency \(M_{BV}\).