# Investigation on Ship Hydroelastic Vibrational Responses in Waves
## 5 Conclusions  
The present research proposes a 3D time domain nonlinear hydroelastic method to numerically estimate the vibrational responses of a large ship advancing in regular and irregular waves. A self-propelled segmented ship model was designed and tested in a towing tank to validate the numerical method presented in this study. The main findings from the presented experimental and numerical studies are as follows:  
1. The presented time domain 3D nonlinear hydroelastic method is capable of predicting the hydroelastic vibrational responses of motions and vertical bending moments of large ships with pronounced bow flares sailing in both regular and irregular waves. The numerical results of motions of heave and pitch and \(M_{BV}\)s are satisfactorily validated by the results of self-propelled segmented model tests. 2. By comparing numerical and experimental results of heave and pitch responses in regular waves, evident oscillations in experimental peaks and troughs of motion responses can be detected due to the effect of velocity change and the uncertainty associated with the generation of experimental regular waves. Small asymmetric characteristics in peaks and troughs can be found in motion responses because of the nonlinearity associated with the hull geometry. Moreover, compared with the low frequency and high frequency components, the total \(M_{BV}\)s show significant asymmetric characteristics in peaks and troughs resulting from the contribution of ship hull geometry nonlinearity and the high frequency slamming components. 3. Either large wave amplitude or high ship velocity will increase the occurrence frequencies of slamming events in irregular wave conditions. Compared with ship velocity, the wave amplitude plays a more important role in the determination of \(M_{BV}\)s. The slamming phenomena have  
Figure 30: Relationship between low frequency \(M_{BV}\)s and total \(M_{BV}\)s. (**a**) Experimental result for irregular condition 1; (**b**) Numerical result for irregular condition 1; (**c**) Experimental result for irregular condition 2; (**d**) Numerical result for irregular condition 2.  
relatively small influence on heave and pitch motions, while they have significant effects on \(M_{BV}\)s. The high frequency \(M_{BV}\)s caused by slamming largely increase the total \(M_{BV}\)s on the basis of low frequency \(M_{BV}\)s, contributing greatly to the asymmetric characteristics of the total \(M_{BV}\)s in irregular wave conditions. Therefore, the slamming loads should be given more attention at ship design stage for structural design and evaluation. 4. For irregular wave conditions, the current research focuses on the statistical parameters of ship hydroelastic responses, since the experimental and numerical irregular waves are just compared statistically. The future study should compare the numerical and experimental irregular waves in fine details of their time series by monitoring the near-ship experimental irregular waves, and therefore, the experimental and numerical ship vibrational responses can be compared in fine details. In this way, some uncertainties associated with the randomly-generated irregular waves can be reduced, which currently results in the evident difference between experimental and numerical statistical parameters of ship responses. In addition, the evident difference between the numerical and experimental mean values of ship responses in irregular waves indicates that, before each run of the ship model, the water surface should be sufficiently calm to reduce the error associated with the choice of the balance position of the ship model. [PERSON] and [PERSON] conceived and designed the experiments; [PERSON] and [PERSON] performed the experiments; [PERSON], [PERSON], [PERSON] and [PERSON] analyzed the data; [PERSON], [PERSON] and [PERSON] wrote the paper. This research was funded by the National Natural Science Foundation of China (NO. 51679049), the China Postdoctoral Science Foundation (NO.