## 3 Results
### Large Amplitude Vibrations of the Wet System
Two points of interest are also emphasised in Figures 12 and 13: point **A** represents the step release event, and point **B** represents the point in time when the wet system reaches \(A_{1}=2.5\) g.  
The frequency variation trends are similar between the two cases, as seen at the top in Figure 13. Both vertical and horizontal error bars are now included, as there are small variations in both amplitude and frequency/damping among the three repetitions. The system starts with a frequency that steadily increases with the decreasing acceleration (and displacement) amplitude together with the substantial decrease in damping ratio and some possible other phenomena (e.g., structural nonlinearity, added mass effect due to the absence of in-vacuo conditions). In the bottom part of the same figure, the damping ratio of component 1 is shown as a function of the acceleration amplitude too. It is interesting to first note that significant differences in \(\zeta_{1}\) are seen starting with the very first data point, unlike the amplitudes \(A1\). The reason for this is that, in the system identification procedure, \(A_{j}\) represents the amplitude at the beginning of the time bin, while \(\zeta_{j}\) is characteristic of the entire two-period bin. While the amplitude \(A1\) indeed does not change substantially in the first half-cycle of the motion, the damping ratio encapsulates information from the later times as well, where the liquid does have an effect. Since it was found that at least two periods of motion must be considered in order to reliably identify the time-localised damping measure of the first frequency component, this behaviour is a natural consequence of this type of analysis. Point **B** in Figure 13 has a different position in the dry and wet cases since the different decay rates imply the reach of distinct amplitudes at the same time instant. In the 50% fill case, between points **A** and **B**, \(\zeta_{1}\) occupies a relatively narrow region, while after point **B** it decreases with a near-linear trend. Similar damping trends were observed in 1 DOF  
Figure 13: Component 1 frequencies and damping ratios vs. component 1 acceleration amplitude, 50% filling level and dynamically equivalent dry case. Error bars show the variability between test repetitions. The amplitude decays following the step release event at **A**. experiments [5], with regions of almost constant damping ratio characterising the violent vertical sloshing region denoted as R1. Single degree of freedom experiments also indicated that the damping ratio starts to decrease at even larger amplitudes of motion [6]. The same phenomenon will be investigated here using the numerical model that was developed based on the 1 DOF experiments. A modulation effect can also be seen in all three identified quantities--amplitude, frequency and damping, shown in Figures 10, 12 and 13. The identified modulation frequency is \(f1\), and it appears to be more pronounced in the wet case. This effect is a manifestation of the internal nonlinear dynamics, which was already observed in the form of the frequency sidebands shown in Figure 9. Owing to its presence with the differing intensities between the dry and wet cases, this effect is influenced by both structural and fluid-structure nonlinear interactions.