## 4 Results and Discussion
Indeed, one of the main difficulties in modelling such an interacting system is the ability to properly define an equivalent mass actively participating in the overall sloshing process, that is to say having active or passive effects on the oscillating motion in the fluid-structure interaction. Another fundamental insight from Figure 10 is again the overall behaviour of the sloped bottom tank. While the flat and circular cases follow a monotonic increasing trend, the sloped one appears to be almost constant until the water depth reaches 9 cm. This is due to the fact that until the water motion is affected by the sloped shape of the bottom side, the sloshing response remains substantially steady. In this sense, the sloped-bottom behaves like a softening spring because of the nonlinear effect of the wave run-up onto the sloping surface. This behaviour plays a crucial role in assessing that the use of slope shaped wedges guarantees a wider range of force impulses, that is to say a wider possibility to find constant tuning. Such a geometrical solution for the bottom of the tank results in the best option for a damping sloshing device. Evidence of the above description can be found in the fundamental damping effectiveness related to the application of the three different bottom geometries. The damping mechanism depends on the amplitude of fluid sloshing and wave breaking patterns. The main driving mechanism of damping is attributable to viscous actions along the boundary layer near the bottom surface and the side walls of the tank and the sloshing motion of the free surface layer of the water, from which comes the importance of testing the behaviour under different bottom geometries. One of the issues, mainly in terms of proper modelling, is that a damper, deep water is not favourable because a large portion of the water does not participate in the damping mechanism. The damping ratio, \(\zeta\), is plotted in Figure 11 against water depth ratios. The following peculiar aspects can be drawn:  
* the flat bottom shaped tank base is the least dissipative geometry, while the sloped one is the most;
* the circular bottom geometry is the most sensitive to the variation of the volume (mass) of water;
* only the sloped bottom seems to show a slightly concave trend with respect to the x-axis. The first result was expected as anticipated and widely reported in literature [16; 20; 33]. The circular shape facilitates the liquid motion and, as a consequence, the mass of water interferes with the optimal tuning, depending on the liquid depth, producing alternatively a higher or lower dissipation. One interesting point concerns the fact that the flat and circular shapes exhibit a convex, flattening behaviour with the increasing water depth, whilst this is not observed for the sloped one. In terms of damping potential, the sloped bottom has a stronger sensitiveness to liquid mass, showing that this type of bottom geometry might affect the motion of the mass of water even at heights greater than the wedge vertical dimension. These considerations lead to the evidence that the sloped geometry might appear to have a contrasting behaviour: it has a more dissipative behaviour but it also shows a reaction delay with respect to the driven impulsive force. This \"_relaxation_\" in time can be seen as a consequence of the _beating_ phenomenon that, in turn, can give an actual measure of the responsiveness of the overall system of _liquid mass \(+\) structure_.