# Investigation on Ship Hydroelastic Vibrational Responses in Waves
## 4 Analysis of Numerical and Experimental Results
### Hydroelastic Responses in Irregular Waves
#### 4.4.2 Motions in Irregular Waves  
The ship responses during a short-term period of 1 h are simulated by the numerical calculation to obtain enough sample data for the subsequent statistical analysis. Since the length of the towing tank is not long enough for the collection of sufficient experimental sample data in a single run of the ship model, a total of 8 runs of the ship model for each irregular wave condition were conducted. Then, the total time series were obtained by connecting the measured time series of each run in the same sea state, thus providing enough experimental data for the following analysis. The time series of heave and pitch motions at CG of the full-scale ship within 1000 s are qualitatively compared from Figures 23-26. Note that in the present research, the experimental and numerical irregular waves are independently randomly generated according to the same target ISSC wave spectra, and thus, the experimental and numerical details of the component regular waves, namely, the wave amplitude and initial wave phase of each component regular wave, may be different because they are inherently probabilistic. The elevation of the irregular waves is, in fact, generated by assigning a random initial wave phase to each regular wave component during the numerical simulation. Since the time series of \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Condition 1 (H\({}_{10}\) = 18.5 m, Tz = 12.5 s)**} & \multicolumn{3}{c}{**Condition 2 (H\({}_{13}\) = 9.185 m, Tz = 11.5 s)**} \\ \cline{2-7}  & **Experiment** & **Target** & **Error (\%)** & **Experiment** & **Target** & **Error (\%)** \\ \hline Significant wave height H\({}_{1/3}\) (mm) & 277.504 & 289.063 & \(-\)4.0 & 139.891 & 143.516 & \(-\)2.53 \\ \hline Characteristic wave period Tz (s) & 1.609 & 1.563 & 2.94 & 1.413 & 1.438 & \(-\)1.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of irregular wave parameters at model scale. Figure 21: Experimentally measured time series of irregular wave condition 2. Figure 22: Comparison of wave spectra. (**a**) Irregular wave condition 1; (**b**) Irregular wave condition 2.  
experimental and numerical irregular waves differ in fine details, the consequent experimental and numerical time series of hydroelastic motion responses will accordingly not agree in fine detail as demonstrated from Figures 23-26. In comparison, the experimental and numerical results of heave and pitch responses respectively show similarity in trends and magnitudes, qualitatively verifying the validity of the numerical prediction, but still indicating the need for statistical analysis. Figure 23: Heave responses in irregular wave condition 1. (**a**) Experimental result; (**b**) Numerical result  
Figure 24: _Cont._  
Figure 24: Pitch responses in irregular wave condition 1. (**a**) Experimental result; (**b**) Numerical result  
Figure 25: Heave responses in irregular wave condition 2. (**a**) Experimental result; (**b**) Numerical result  
The statistical parameters of the hydroelastic motion responses are adopted to describe the ship responses in short-term irregular waves. The comparison of statistical parameters by measurement and calculation is listed in Table 7. Note that for both irregular wave conditions, we present the mean values of heave and pitch responses without calculating the relative errors. This is because the experimental mean values of both heave and pitch motions contain inevitable experimental uncertainties mainly associated with the initial experimental conditions. For each run, we have to choose the initial position of the ship model as the balance position relative to which the heave and pitch responses are experimentally measured. The realistic water surface in the towing tank after each run always contains small ripples that slightly move the ship model from its theoretical balance position used in numerical simulation. It is this experimental error that makes the mean values of experimental heave and pitch motions greatly deviate from those obtained numerically.