# The Effect of Porous Media on Wave-Induced Sloshing in a Floating Tank
## 4 Results and Discussion
### Sloshing in a Tank Filled with Porous Media: EL Method vs. Mechanical Model
It is important to take the nonlinear effect into account since it changed the pitch amplitudes of the body in this example. The phase cancellation appeared. Since the sloshing-induced moment was comparable to the wave-induced moment, the moment cancellation was fairly strong. The body responses and sloshing reactions by the SDOF and five-DOF mechanical systems were identical for the surge, heave, and pitch motions. This shows that the fundamental mode dominated and the high-mode sloshing responses were too small to affect the FSI behavior. It justifies the design strategies for the liquid dampers that only emphasized the first modal response [22]. Figure 11: The vertical forces acting on the floating body for the large-wave case. Figure 12: The pitch motion responses of the floating body, configured with a water tank installed with porous media, undergoing large wave excitation. When the small wave excitation was applied, the body motions and the resultant forces along three directions are shown in Figures 14-19. The overall trends were similar to what was observed for the large-wave cases. However, the smaller wave loadings caused a smaller body vibration, hence lowering the nonlinear effect in the sloshing reactions. The mechanical model captured the pitch motion more easily. Similarly, the resultant forces and body dynamics by the SDOF and five-DOF mechanical systems highly coincided. Figure 6:0 The surge motion responses of the floating body, configured with a water tank installed with porous media, undergoing small wave excitation. Figure 6:1 The overturning moments acting on the floating body for the large-wave case. The response spectra of the body motions for the large- and small-wave cases are shown in Figures 20 and 21, respectively. The spectra by both methods are very similar, hence the mechanical model ensured the consistency of the dynamic characteristics of the sloshing behavior. The response spectra by the SDOF and 5-DOF mechanical systems are also identical, so the importance of the first modal response was validated in the frequency domain. Both methods showed one peak at the resonant frequencies for each motion, but the EL method observed another local peak at the double frequency (1.16 Hz) of the angular frequency (1.16 Hz) of the angular frequency (1.  
response spectra. This means the nonlinear effect due to the convective term appeared. No peak at the double frequency was observed by the mechanical model because the nonlinear effect was neglected. However, this phenomenon was not obvious in the small-wave case as shown in Figure 6:2 Besides, the response spectra of the surge and heave motions had no local peak at the double frequency. The nonlinear sloshing response was negligible in these two vibration modes. Figure 6:3 The vertical forces acting on the floating body for the small-wave case. Figure 6:4 The pitch motion responses of the floating body, configured with a water tank installed with porous media, undergoing small wave excitation. Figure 6:5 The overturning moments acting on the floating body for the small-wave case. Figure 6:6 The response spectra of the floating body, configured with a water tank installed with porous media, undergoing large wave excitation. The free-surface elevations on the left-side (stern side) wall of the tank for the large- and small-wave cases are shown in Figure 6:7 Note that in the mechanical model, the free-surface elevation of the sloshing fluid can be obtained by:  
Figure 6:8  
In the large-wave case, the EL method could simulate nonlinear waves. The mechanical model showed linear waves and overestimated the amplitude due to the lack of nonlinear damping. Similar results have been observed in past experiments [25]. In the small-wave case, the wave elevations by both methods were still different. However, it only slightly changed the sloshing forces. Besides, the five-DOF system included more high-mode sloshing responses than the SDOF system. It gave a higher hydrostatic pressure but those components were too small to affect the FSI simulation.