# Investigation on Ship Hydroelastic Vibrational Responses in Waves
## 4 Analysis of Numerical and Experimental Results
### Modal Analysis
#### 4.3.2. Motions in Regular Waves  
The experimental and numerical hydroelastic responses of heave and pitch at CG of the target ship are extracted and analyzed for the two regular wave conditions. Figures 14 and 15 display the comparison of motion responses in the two testing conditions. The experimental heave and pitch responses show some oscillations in both peaks and troughs compared with the numerical results. This is because the phenomenon of forward speed fluctuation of ships in waves can naturally occur in the present self-propelled ship model experiment, while the present numerical method assumes that the ship velocity remains unchanged during the whole simulation process. In addition, since the experimentally-generated wave peaks (or wave troughs) slightly differ from each other as illustrated in Figure 13, the ship model motion responses under such experimental waves will consequently show some difference in their peak values and trough values, as demonstrated in Figures 14 and 15. The numerical results slightly overestimate the heave and pitch responses on average compared with the experimental results, as can be found in Figures 14 and 15, probably due to the omission of dissipation effects associated with fluid viscosity in the current numerical methodology. Figures 14 and 15 show that, on average, the peak values and trough values of heave response are nearly symmetric. In comparison, both the experimental and numerical trough values of pitch response are larger than peak values. This phenomenon results from the joint effect of nonlinearity of the ship hull geometry and the dynamic effect of waves. Here, negative pitch values represent the trim by stern, meaning that in the present case the specific ship hull geometry tends to lift the ship bow region a little bit in waves. The experimental results of both heave and pitch responses include some minor noise due to the friction and vibration of the motion monitor apparatus. In general, the numerical results agree satisfactorily with the experimental results. agree pretty satisfactorily, with some discrepancies being found between numerical and experimental hogging \(M_{BV}\)s which are due to the limited nonlinear factors considered in the numerical method. The peak values of numerical high frequency slamming \(M_{BV}\)s are also overestimated compared with the experimental results; see Figure 19.  
Figure 20 shows the relationship of hogging and sagging values of \(M_{BV}\)s with respect to wave heights at the ship speed of 18 km. As can be seen clearly from Figure 20, the total \(M_{BV}\)s, low frequency \(M_{BV}\)s and high frequency slamming \(M_{BV}\)s all vary nonlinearly with the increase  
Figure 19: High frequency \(M_{BV}\) in regular waves. (**a**) Regular wave condition 1; (**b**) Regular wave condition 2. Figure 17: Total \(M_{BV}\) in regular waves. (**a**) Regular wave condition 1; (**b**) Regular wave condition 2  
Figure 18: Low frequency \(M_{BV}\) in regular waves. (**a**) Regular wave condition 1; (**b**) Regular wave condition 2.  
of the wave height. Compared with the hogging and sagging values of the total \(M_{BV}\)s and low frequency \(M_{BV}\)s, the magnitudes of peaks and troughs of the high frequency slamming \(M_{BV}\)s are much closer; see Figure 20c. The evident difference between the absolute values of the hogging and sagging \(M_{BV}\)s for the total \(M_{BV}\)s and low frequency \(M_{BV}\)s is mainly due to the nonlinear effect of the change of wet hull geometry on which the wave pressure acts for a relatively long duration in every incident wave period.