# Investigation on Ship Hydroelastic Vibrational Responses in Waves
## 4 Analysis of Numerical and Experimental Results  
The experimental results and the numerical results are compared and analyzed in this section. For the structural part, the ship structure is modeled by 20 beam elements and the first three elastic modes of vertical bending are used for the solution of structural response. For the hydrodynamic part, a total of 2380 panels are generated by dividing the whole ship hull surface for the computation of nonlinear [F\({}_{I}\)] and [F\({}_{H}\)]. To calculate the linear [F\({}_{R}\)] and [F\({}_{D}\)], the wet contact surface of the hull in still \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Capacity** \\ \hline Carriage speed (m/s) & 0.1– 6.0 \\ Wave period (s) & 0.4– 4.0 \\ Wave natural circular frequency (rad/s) & 1.57– 15.70 \\ Wave length (m) & 0.25– 24.99 \\ Maximum regular wave height (m) & 0.4 \\ Maximum irregular significant wave height (m) & 0.32 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Capacities of the towing tank. Figure 4: The ship model towing tank. (**a**) Wave tank at work; (**b**) Wave generator  
Figure 3: General arrangement of elastic backbones. water is divided into 2256 panels. Nonlinear [\(\mathbf{F}_{SL}\)] is computed based on 22 unevenly-distributed cross sections. Several experimental conditions are selected for the comparison and analysis in this paper, which are listed in Table 3. Note that the two regular wave periods presented in Table 3 correspond to the relation of \(\mathcal{NL}=1.0\), where \(\lambda\) and \(L\) respectively denote the wave length and the length waterline of the ship. Figure 5 demonstrates the total panels of the whole ship surface and the partial panels under the calm water surface. Figure 6 presents the extracted cross sections along the hull for slamming loads estimation. The calculation of nonlinear [\(\mathbf{F}_{I}\)] and [\(\mathbf{F}_{H}\)], as introduced in Section 2.3, is based on the instantaneous wetted hull surface, the acquisition of which can be accomplished by two steps, as illustrated in Figure 7. The first step is to obtain the so-called physical instantaneous wetted surface by intersecting the deformed ship hull panel with the incident wave profile; see the upper part of Figure 7. In this step, special care should be given to those panels whose vertices are neither all below nor all above the incident wave profile. For panels of this kind, the two intersection points between the incident wave profile and the panel sides are joined together by a straight line segment. If the remaining panel is neither a triangle nor a rectangle, then it is further subdivided into a triangle  
Figure 5: Mesh information. (**a**) Panels of the whole hull surface; (**b**) Panels of the wet surface for [\(\mathbf{F}_{R}\)] and [\(\mathbf{F}_{D}\)]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Wave Conditions** & **Vessel Speed V (kn)** & **Wave Height H (m)** & **Wave Period T (s)** \\ \hline Regular wave condition 1 & 18 & 4.8 & 13.28 \\ \hline Regular wave condition 2 & 18 & 9.6 & 13.28 \\ \hline
**Wave Conditions** & **Vessel Speed V (kn)** & \
\begin{tabular}{c} **Significant Wave** \\ **Height H\({}_{1/3}\) (m)** \\ \end{tabular} &
\begin{tabular}{c} **Characteristic Wave** \\ **Period Tz (s)** \\ \end{tabular} \\ \hline Irregular wave condition 1 & 5 & 18.5 & 12.5 \\ \hline Irregular wave condition 2 & 18 & 9.185 & 11.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental conditions extracted for analysis. Figure 6: Uneven cross sections for calculation of slamming loads. panel and a rectangle panel. After this first step, a satisfactory physical instantaneous wetted surface is acquired because the difference between the straight line segment and the wave profile within the panel is very small.