# Research on Influence of Tank Sloshing on Ship Motion Response under Different Wavelengths
## 6 Conclusions and Discussions  
The purpose of the present research was to explore the effect of tank sloshing on the response to ship motion. Therefore, the pitching and rolling motions of ships with different liquid loading rates under different incident wave wavelengths were respectively calculated. The major results are summarized as follows:  
1. In the head sea condition, the sloshing of the tank has little effect on the pitching motion of the ship. The main reason is that under this condition, the sloshing moment of the tank is much smaller than the external wave moment. 2. In the head sea condition, the wavelength of the incident wave has a great influence on the pitching motion of the ship. When the incident wave wavelength is close to the length of the ship, it is a dangerous situation because the pitching motion of the ship is the most violent (large amplitude and short period). 3. When the liquid loading rate is not very high, the sloshing of the tank will reduce the natural frequency of the ship's roll. The higher the liquid loading rate is, the lower the natural frequency of ship roll will be. This is mainly because the phase of the tank sloshing moment is always opposite to the external wave moment, which reduces the ship's restoring moment. 4. When the liquid loading rate is very high, since the free liquid surface is close to the top of the tank, the sloshing moment of the tank decreases, and its influence on the natural frequency of the ship's rolling motion decreases. 5. The sloshing of the tank has a significant effect on the rolling motion of the ship under the condition of transverse waves. The effect of tank sloshing on the rolling motion \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Liquid Loading Rate**} & **Roll Natural Frequency** & **The Ratio of Natural Frequency to** \\  & **(rad/s)** & **Incident Wave Frequency** \\ \hline
0.8 & 2.417 & 0.754 \\
0.4 & 2.705 & 0.844 \\
0 & 3.634 & 1.134 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Ratio of ship roll natural frequency to incident wave frequency when incident wave wavelength is 6 m. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Liquid Loading Rate**} & **Roll Natural Frequency** & **The Ratio of Natural Frequency to** \\  & **(rad/s)** & **Incident Wave Frequency** \\ \hline
0.8 & 2.417 & 1.021 \\
0.4 & 2.705 & 1.143 \\
0 & 3.634 & 1.535 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Ratio of ship roll natural frequency to incident wave frequency when incident wave wavelength is 11 m. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Liquid Loading Rate**} & **Roll Natural Frequency** & **The Ratio of Natural Frequency to** \\  & **(rad/s)** & **Incident Wave Frequency** \\ \hline
0.8 & 2.417 & 1.192 \\
0.4 & 2.705 & 1.334 \\
0 & 3.634 & 1.793 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Ratio of ship roll natural frequency to incident wave frequency when incident wave wavelength is 15 m.  
of the ship is realized by changing the natural frequency of the rolling motion of the ship. The closer the incident wave frequency is to the natural frequency of ship roll, the greater the ship's roll amplitude will be. In this paper, the CFD method is used to simulate the motion of a liquid-carrying ship under different waves. The results calculated by the numerical model are close to the experimental values, but some limitations exist. For example, the influence of tank bulkhead deformation and hull deformation is not considered. Further study is required to refine the model and make it closer to reality. [PERSON] made the computations, data analysis and wrote this paper; [PERSON] did the proof reading. [PERSON] guided the whole project. All authors have read and agreed to the published version of the manuscript.