Due to the dynamic loadings of train traffic, railway bridges are subjected to vibration stresses.The progressive expansion of high-speed rail networks and the growing axle loads in freight trafficare causing an increase in vibration excitation. The effects affect both railway operations and bridge structures, as well as the vehicles themselves. In connection with this, the risk of material fatigue in supporting structures, excessive deformation responses increases and issues such astrack misalignment or loosening of the ballast bed occur.Furthermore, it is the responsibility of the infrastructure manager to ensure the operational safety of bridges, which is, among other things, demonstrated by dynamic calculations. From anormative perspective, the verification is deemed fulfilled when the maximum vertical accelerations of the bridge w ̈max (calculated from the vibration predictions), do not exceed an allowable limit w ̈z ul. Otherwise, measures such as speed reductions are ordered, which can have a negative impact on traffic mobility. In general, the magnitude of the maximum vertical acceleration w ̈maxis influenced by numerous input parameters. This includes the traveling speed and axle loads of the train, the characteristics of the bridge (such as its span, stiffness, natural frequency, type ofdesign and construction), as well as the foundation and soil conditions. Also of great importanceis the damping factor ζ, which describes the damping properties of the bridge. A high dampingfactor ζ results in lower vibration intensity.Basically, there are two ways to determine the damping factor ζ: On one hand, this occursaccording to normative specifications (standard case) or through an analytically model-basedcalculation approach; on the other hand, it will be reached by evaluating an in-situ measurementexperiment on real existing structures. The latter is connected with high costs and arises only inindividual cases. Especially the recommendations of the Eurocodes and conservative approachesregarding the regulation of the damping factor ζ show a significant discrepancy with measurementresults. This can cause vibrations to be overestimated by the standard, which could potentiallylead to incorrect operational decisions. At the same time, for example in the construction sector,there is a demand to consider sustainable maintenance measures for existing bridges, which shiftsthe focus to the precise and realistic determination of the damping factor ζ. Currently, this is amajor research focus in the dynamics of railway bridges.For this reason, as part of research projects at the Institute of Structural Engineering / ResearchUnit Steel Structures at TU Wien, the dynamic damping behaviour of the ballast track isbeing investigated in more detail using a large-scale test facility at a 1:1 scale. Based on thepresent measured data, it was possible to abstract an energy-equivalent system with a singledegree of freedom (SDOF system) that has nonlinear properties in the material characteristics(displacement-dependent spring and frequency- and acceleration-dependent damping characteristiccurve). The presently applied method for the computational determination of the dampingfactor only considers the case of approximately estimating the damping factor ζ (= the sumof the damping components from the structure and the ballast track) in a SDOF system withconstant material parameters. Even though the existing linear computational model already shows good agreement compared to empirical measurements, there is still a motivation to reduce the discrepancy between calculation and measurement and to fully utilize the available damping reserves. Therefore, this work primarily focuses on the single-degree-of-freedom system with nonlinear material behaviour and evaluates the influence of nonlinear system properties indetermining the damping factor ζ.The main task of this work lies in solving nonlinear equations of motion in both the frequency and time domains, as well as in generating and evaluating their system responses. All calculationalgorithms are designed to be practical and can serve as a guideline for addressing futurenon linearities. The analyses are based on real bridge structures, whereby different variants are tested depending on the modeling depth. Due to the considerable number of dependent variables in the parameter field, including frequency range, damping factor level, geometry parameters,as well as the amplitudes of acceleration and displacement, the overall picture is compiled step by step in the form of ten defined research questions. A key reference parameter is the relation factor β, which compares the damping factor of the currently used linear SDOF system (state of the art) with the determined damping factor of the nonlinear SDOF system.The central question is therefore, which values the relation factors β assume for different types of nonlinearities (model variants) at selected bridges, and how β differs both in the frequency and time domains. Furthermore, the derived factor β provides the opportunity to adjust the impact of actual nonlinearity on the idealized linear computational model. In the opposite case,there is potential to calibrate the damping coefficient C of the linear computational model based on the results of a real in-situ measurement experiment on existing structures.At the beginning of this thesis, an introduction to the topic and objectives is presented, followed by four sections. In the first part, the theory of linear SDOF systems is illustrated, introducing both classic and new methods for evaluating frequency responses and decay processes for thedetermination of damping factor. The following second section deals with the purely vertically oriented Model 1, whose mechanical behaviour is explained, and further solution strategies are developed. Similarly, the third section deals with Model 2, which fully incorporates the horizontal track-structure interaction. The fourth part summarizes the results and findings. It is shownthat, depending on the model variant and natural frequency, there can be practically no to considerable differences in damping, which can therefore have an impact on the assessment ofbridge safety.