## 5 Conclusions  
This work focused on the presentation of an alternative methodology to assess the damping coefficients using the free vibration records from passing trains in filler-beam bridges, contributing to new developments in the damping assessment in railway bridges. The methodology presented is based in the Prony method with application in the damping assessment in railway bridges. This method has the advantage of estimating the damping coefficients, frequency, phase, and amplitude of each sinusoid comprising the whole signal of the free vibration acceleration record of the passing trains, through decomposition of damped complex exponential sinusoids of the signal. However, when the signal is subjected to a high amplitude of noise, the method tends to have poor behaviour. To overcome this situation, a lowpass filter should be applied to the original data signal to eliminate as much noise as possible that is found in higher frequencies. The energy-sorting technique of the Prony method made it possible to sort each frequency of the complex exponential sinusoid as a function of the energy content of each frequency to identify the dominant frequencies of each signal, which are the ones with the most energy content. This technique reduces the chance of false frequency estimations. The continuity effect of the track causes the free vibration not to start immediately after the train leaves the bridge. The analysis of this effect was done using static and dynamic analyses. The static analysis evaluated the influence line of displacements to analyse the distance for which the load starts to lose influence in the bridge's response. The dynamic analysis evaluated the receptance, considering dynamic impact loads at different distances away from the bridge. These analyses conclude that the distance for which the load has a negligible effect in the response is when the train is approximately 3.0 m away from the bridge. This assumption was used for the damping estimation using the Prony method. The validation of the Prony method using a 3D numerical model through train-track-bridge interaction analyses, using different train speeds and different types of vertical irregularities, was made. A known damping coefficient was imposed to the first two modes of vibration of the bridge, according to the lower limit bound for filler-beam bridges of the EN1991-2. The Prony method proved to be capable to accurately identify the frequencies and damping coefficients of the numerical model, using the free vibration periods from the interaction analyses. The method has also shown efficiency in identifying  
Figure 18: Damping coefficient values in the function of the bridge span length (red) and the comparison with the ERRI D214 database [1] and the lower limit for damping coefficients for filler-beam bridges from the EN1991-2 [2]. frequencies and damping coefficients when coupled modes of vibration are presented in the free vibration periods. The experimental assessment of the damping coefficients was performed in four filler-beam railway bridges of the Portuguese Railways Network. These tests evolved ambient vibration tests to achieve the modal parameters of the presented bridges, useful to the application of the Prony method. The tests under railway traffic allowed the identification of the dynamic response in terms of accelerations of each bridge due to the passage of trains. The results obtained in these tests made it possible to estimate the frequency and damping of each bridge due to the passing trains. The work developed allowed a different approach of analysis of damping coefficients in railway bridges, highlighting the dominant frequencies that are mobilized after the train's passage and its respective damping.