## 1 Introduction  
Atmospheric turbulence or gusts produce significant deformations when they encounter highly flexible structures such as aircraft wings. These deformations can reach 20% of the wing span in some severe cases. The fuel tanks, which are placed inside the wings, carry a weight of fuel comparable to the oscillating structural components. The current engineering practices for wing design do not include the dynamical effects that the fuel produces within the tanks, which could affect the aircraft design loads. The major experimental tests to identify and verify the dynamic characteristics of the aircraft structure (Ground Vibration and Flight Flutter tests) are limited to small amplitudes and barely excite significant sloshing modes. In this context, the EU-SLOWD research project [1; 2] aims to study how much fuel sloshing affects the structural damping of the wing oscillations. One of the main ideas of the SLOWD project is to present a comparable set of experimental and numerical campaigns based on scaled and simplified experiments that could predict some quantitative results up to a full-scale wing experiment, where the amplitudes are large enough to produce relevant sloshing effects. During this project, a large number of experimental and numerical studies have been produced. Despite that violent sloshing is a highly nonlinear phenomenon, some early theoretical approaches to the problem are found in this field; see, for example, the classical references [3; 4; 5]. In terms of experimental results, the first studies were based on a partially filled tank attached to an oscillating cantilever beam, which demonstrated that the extra damping that appears is due to the sloshing motion; see [6; 7]. This extra damping was measured in terms of decrements on the tip beam acceleration. In this experiment, a baffled water tank was mounted on a 2.35 m cantilever which is broadly representative of a wing and its fuel tanks. The cantilever is forced into a deflected shape and suddenly released, such that the free beam decaying oscillations are recorded by several accelerometers while the forces between the beam and the tank are measured by load cells. Based on these promising results, and taking into account that the damping of the tank acceleration and the vertical sloshing force that interacts between the liquid and the tank are the two most relevant outcomes from the experiment, a similar [PERSON] multi-scale campaign was carried out at the Model Basin Research Group Sloshing Laboratory of the UPM in Madrid, Spain; see [8]. In this work, an experimental methodology is developed to quantify the kinematics and the sloshing forces on a vertical Single Degree Of Freedom (SDOF) tank excited with real wing accelerations. These experiments confirmed again that the fluid sloshing increases the global damping of the system notably, finding that the slosh-induced damping force includes an inertial term and a dissipative term. An important conclusion obtained was that the time shift between the force impacts and the tank maximum displacement is a very relevant magnitude in fluid-induced energy dissipation. Another experimental campaign based on a release test of a vertically vibrating structure again confirmed the additional damping created by the sloshing motion; see [9]. These experiments show that the damping depends on the amount of fluid in the tank and the initial maximum acceleration. In this experiment, where the tank is not guided vertically and the structural damping is reduced, three distinct response regimes corresponding to different motions of the fluid are observable during the transient decay, the starting one being the most important in the overall energy dissipation. Other experimental campaigns where the tank is moved periodically with different amplitudes and frequencies and the sloshing force and the tank kinematics are measured are performed in [10; 11; 12]. The other methodology used to study violent sloshing flows is the computational one, where different numerical techniques can be applied.