## 1 Introduction  
Railway bridges are structures in which the dynamic effects induced by traffic loads can reach significant values, especially for speeds higher than 200 km/h [1, 2]. The magnitude of the dynamic effects largely depends on the characteristics of the train-track-bridge system and their interfaces [3]. From the track-bridge system, the stiffness, mass, and damping properties are particularly relevant, both from the bridge and track, while from the train subsystem, the speed, the loading scheme (i.e., number of axes, axes, axes spacing, and loads values), as well as the values of the sprung and unsprung masses, are important parameters [4, 5]. Regarding the wheel-rail interface, the characterization of the track irregularities profiles and wheel defects (e.g., wheel flats and polygonization) are also relevant [6, 7]. In what specifically concerns damping in railway bridges, its accurate evaluation is crucial since this parameter strongly influences the maximum dynamic response under railway traffic, particularly in resonance or near resonance scenarios [8]. However, most of the conventional and high-speed traffic operates at speeds that are not susceptible to causing the resonance phenomena. [PERSON] et al. [9] state that during bridge crossing by trains, several damping mechanisms, more specifically, energy dissipation mechanisms, occur with different levels of complexity and importance. Furthermore, these energy dissipation mechanisms are derived from the different subsystems and their interfaces, mainly at the: (i) bridge, (ii) track-bridge interface, (iii) bridge-soil interfaces, and iv) train-bridge interface. At the bridge, the energy dissipation is associated with the material damping closely associated with the amplitude of the deflections of the bridge deck. Additionally, the dissipation of energy within materials is usually relevant in the case of composite bridges, as well as the materials deterioration due to ageing mostly associated with relative movements at cracks [1]. [PERSON] et al. [10] state that several non-structural components can increase the damping capacity, such as the bridge and rail expansion joints, the bearings, and handrails [11]. In the case of friction bearings, due to rotation of the deck and the bearing eccentricity in relation to the deck axis, the damping is derived from the cyclic longitudinal displacements on the supports. More recently, in the retrofitting of existing railway bridges, the use of fluid viscous dampers to reduce the vertical acceleration levels allowed an additional energy dissipation effect, through hysteresis cycles, during the train passages [12; 13; 14]. Concerning the track-bridge interface, the damping is mainly associated with the longitudinal relative displacements occurring between the rail and deck through the ballast layer, allowing the transmission of longitudinal stresses between these two elements. The nonlinear behaviour of the track-deck interface is responsible for a very important energy dissipation mechanism, mainly at short/medium span bridges [11; 15]. Inclusively, this effect can be responsible for the existence of non-proportional damping, increased complexity of the bridge mode shapes, and damping ratios [16; 17]. Additionally, [PERSON] et al. [18], [PERSON] et al. [19] and [PERSON] [20] showed that the damping is influenced by the seasonal (summer/winter) weather conditions due to freezing of the ballast layer, especially in railway lines not heavily trafficked. At the bridge-soil interfaces, due to the soil-structure interaction (SSI) phenomena, there is an important energy dissipation by irradiation to the underground and adjacent terrain, particularly at the foundations and abutments [1; 21; 22]. Regarding the train-bridge dynamic interaction, there is an energy dissipation due to track-induced vertical relative displacements caused by the moving train [23]. This type of energy dissipation occurs both in the embankment and in the ballasted track on the bridge.