## 3 Results
### Large Amplitude Vibrations of the Wet System  
For the wet analysis, the 50% filling level case was considered with the solid-section baffles. An initial overview of the differences between the dry and wet systems can be seen by inspecting the tank tip acceleration versus time for the two cases. These results are shown in Figure 11, where the time parameter was normalised by \(T_{1}\). The mean values  
Figure 10: The amplitude, frequency and damping ratio of the first frequency component (component 1) of the acceleration time series measured throughout the fuel tank, dry case. Figure 9: Frequency response function for the dry and wet systems. The NLS-identified dry system is shown in green for comparison. among the three repetitions are shown with the black curves, and the red/grey bands indicate the minimum and maximum acceleration values. Insets are included showing the detailed views at the selected times. The differences between the dry and wet cases in the first part of the transient are not noticeable. When the response progresses, the amplitude of the wet system drops faster as a first indication of the induced damping effects due to sloshing. Similar trends were noted in a simpler single degree of freedom transient sloshing tests [5]. There are also multiple frequency components noticeable immediately following the step release event, which decay at rates that are different between the dry and wet cases until the point when only the first frequency component is observable. Small phase shifts, which are indicative of the frequency differences, can also be observed when comparing the dry and wet systems. These aspects can be investigated further by decomposing the signal into its components using the NLS procedure. Figures 12 and 13 show the amplitudes, frequencies and damping ratios for the acceleration component corresponding to the first bending mode. Since the damping ratios for the wet and dry cases are different, the same acceleration values will be reached at different times, so the frequency and damping values are shown as a function of the component amplitude for comparison purposes. The tank tip acceleration across the three repetitions was used for this analysis, the markers and error bars having the same significance as before. Figure 11: Typical sloshing response of the MiniWoT structure, 50% filling level case compared to dynamically equivalent dry case. Figure 12: Amplitude of component 1 vs. normalised time, 50% filling level case and dynamically equivalent dry case. Error bars show the variability between test repetitions. Starting with the second half of the first period of motion, a distinct drop of component 1 acceleration amplitude can be seen in Figure 12 for the wet case when compared to the dry case. It is interesting that this is not immediately obvious by inspecting the complete time series in Figure 11, the reason being that component 1 of the signal conveys only fractional information about the overall motion characteristics in the first cycle of motion (5.5 g of the 15 g peak acceleration). Other frequency components of the signal are thus seen to be dominant in the first part of the transient response. An initial half-period delay is noticeable for the wet case \(A1\) amplitude to deviate and decrease below the dry response. This can be understood by studying these trends in conjunction with the liquid movement (this analysis will be conducted in Section 4). The differences in the amplitude components increase substantially afterwards. This is indicative of significant sloshing-induced dissipative effects influencing the first out-of-plane bending response component associated with mode \(F1\).