## 1 Introduction  
Aircraft designed and developed in the European zone must comply with the certification specifications of the European Aviation Safety Agency (EASA). According to the Certification Specifications for Large Aeroplanes (CS-25) Acceptable Means of Compliance (AMC), the structural dynamic model of the aircraft may include damping information: _\"In the absence of better information it will normally be acceptable to assume 0.03 (i.e., 1.5% equivalent critical viscous damping) for all flexible modes. Structural damping may be increased over the 0.03 value to be consistent with the high structural response levels caused by extreme gust intensity, provided justification is given.\"_[1]. The value of the structural damping may be increased if justified, and a larger value of structural damping may lead to a less conservative structural design through reduction in the peak loads and/or improving the fatigue life of certain components. These improvements, in turn, lead to a more efficient use of materials, reduced weight and improved fuel burn, in line with the current trends toward a reduction in the environmental impact of aviation (e.g., the ATAG net-zero carbon goal by 2050 ([[https://www.atag.org/component/news/?view=pressrelease&id=125](https://www.atag.org/component/news/?view=pressrelease&id=125)]([https://www.atag.org/component/news/?view=pressrelease&id=125](https://www.atag.org/component/news/?view=pressrelease&id=125)), accessed on 12 July 2022)). A conventional approach for aircraft load alleviation uses control surfaces (often spoilers or ailerons), actuated using an active control law to reduce the dynamic response of the aircraft to gusts and manoeuvres. More recently, there have been proposals for passive load alleviation using tow-steered composites [2] or folding wing-tips [3]. Another possible candidate for reductions in dynamic aircraft loads is fuel sloshing inside wings, taking into account and exploiting the movement of the fuel inside large aircraft wings. A net increase in damping may be achieved due to the dynamic interaction between the moving fuel and the wing structure. This work is part of Sloshing Wing Dynamics (SLOWD), an EU-funded project ([[https://slowd-project.eu/project/project_overview](https://slowd-project.eu/project/project_overview)]([https://slowd-project.eu/project/project_overview](https://slowd-project.eu/project/project_overview)), accessed on 12 July 2022) aiming to investigate and exploit fuel sloshing in order to increase the effective damping in aircraft structures. The experimental work presented here is based on extensive previous investigations into systems of reduced complexity, and part of it was also previously presented in [4]. A transient single degree of freedom analysis was conducted in [5], where an experimental analysis supported by two numerical models of varying fidelity showed that (1) vertical sloshing induces substantial damping effects that depend on the tank filling level and amplitude of excitation, and (2) qualitatively and quantitatively, different sloshing dissipation mechanisms are present at large and small amplitudes of excitation. Similar findings were reported in [6]. An in-depth experimental and numerical analysis based on single-frequency harmonic excitation [7; 8] then revealed how the liquid movements relative to the tank affect the observed induced effects. High fidelity numerical models are considered in the SLOWD project, based on Smoothed Particle Hydrodynamics (SPH) and Volume of Fluid (VoF) CFD that have proven their modelling capability on 1 DOF vibrating systems [5; 9] and on beam systems [10]. Multiple reduced-order numerical models for sloshing were considered as well. Vertical sloshing action was modelled using bouncing balls [5], ballistic-harmonic kinematics-based models [7] and bouncing ball models trained on experimental data using neural networks [11].