## 4 Experimental Assessment of Damping Coefficients
### Results of the Experimental Campaigns
#### 4.3.2 Tests under Railway Traffic  
The tests under railway traffic were also performed in the same four filler-beam bridges of the Northern Line of the Portuguese Railways Network. This type of testing is conducted to a measurement of the dynamic response of the bridge, in terms of accelerations caused by the passing trains. The responses were useful to estimate the damping of the bridges through the Prony method described and validated before in Sections 2 and 3, respectively. As for the ambient vibration tests, these were also performed using a typical layout for the sensors consisting of 5 measurement points, as illustrated in Figure 15a, to guarantee a full representation of the passing trains in both railway tracks of the bridge deck. \begin{table}
\begin{tabular}{c c c} \hline
**Bridge** & **First Mode** & **Second Mode** & **Third Mode** \\ \hline Braço do Cortico & & \\ (L = 7.02 m) & & \\  & \(f=18.01\) Hz & \(f=23.65\) Hz & \(f=41.65\) Hz \\  & \(\xi=1.13\%\) & \(\xi=0.75\%\) & \(\xi=1.36\%\) \\ \hline Vale da Negra & & \\ (L = 7.10 m) & & \\  & \(f=15.24\) Hz & \(f=18.56\) Hz \\  & \(\xi=2.12\%\) & \(\xi=1.26\%\) \\ \hline Casalheira & & \\ (L = 11.10 m) & & \\  & \(f=9.50\) Hz & \(f=11.82\) Hz \\  & \(\xi=1.02\%\) & \(\xi=0.60\%\) \\ \hline Canelas & & \\ (L = 6 \(\times\) 12 m) & & \\  & \(f=8.70\) Hz & \(f=9.80\) Hz & \(f=14.90\) Hz \\  & \(\xi=1.90\%\) & \(\xi=1.80\%\) & \(\xi=1.90\%\) \\ \hline \end{tabular}
\end{table} 
Table 5: Results from the ambient vibration tests. The equipment used for the testing consisted of piezoelectric accelerometers to measure the vertical acceleration due to trains' passage, PCB model 393A03 (Figure 15a) with a sensitivity of 1 V/g and a measurement range of \(\pm\)5 g, installed on the bridge deck's lower side. In these tests, accelerometers were used with a higher measurement range, due to the higher acceleration levels imposed by the passing trains. The accelerometers were distributed along the span in the centre of each track, and an additional one (number 3 in Figure 15a) near the joint between the two half-decks. All the accelerometers were placed along the embedded steel beams from the deck. For the detection of the train axles, four optical sensors were installed in the track sleepers, two in each track. These sensors were useful to detect the train axles envisaging the speed estimation and axles spacing, allowing the detection of the precise time instant that the last train axle leaves the bridge, which is decisive to estimate the beginning of the free vibration movement of the bridge (see Section 3.2). Figure 15b represents the location of these sensors in the deck's upper side, with an overview of its installation. Figure 15: Tests under railway traffic typical layouts: (**a**) accelerometers with a detail of the PCB 393A03; (**b**) optical sensors layout with a detail of the sensor (left) and their locations in the tracks (right). The time series of the trains were acquired with a sampling frequency of 2048 Hz and the data acquisition was performed using the cDAQ-9188 system from National Instruments (NI), equipped with IPEE analog input modules with 24-bit resolution (NI-9234). The post processing of the results was performed using the free vibration responses after the train passage, using the Prony method, explained in Section 2, taking into account the sensitivity analysis in relation to the free vibration period and the validation of the Prony method presented in Sections 3.2 and 3.3, respectively. The Prony method is, in some cases, more efficient to estimate the structural parameters of the bridges, especially when the free vibration period after the trains passage is not controlled by the first vibration mode but by coupled modes. Figure 16 presents the results of damping coefficient values extracted from Prony method as a function of the maximum acceleration for the eigenfrequencies. The results consider the different values for two types of trains of the Portuguese Railways.