## 4 Experimental Assessment of Damping Coefficients
### Results of the Experimental Campaigns
#### 4.3.1 Ambient Vibration Tests  
The ambient vibration tests were performed in the four filler-beam bridges of the Northern Line of the Portuguese Railways Network, described in Section 4.2. For all bridges, these tests were performed using a typical and normalized layout for the sensors used in the ambient vibration tests, making it easier to compare the results between the bridges. Due to the bridge length and the fact that it is a six-span bridge, the Canelas bridge adopted a slightly different layout for this kind of test. These tests have the objective of evaluating the vibration modes of the bridges and achieving its modal parameters, namely, frequencies and damping. The typical experimental layout consists of 12 points of measurement, as shown in Figure 13, to guarantee a clear representation of the vibration modes.  
The equipment used for these tests consisted of piezoelectric accelerometers to measure very low levels of vibration (in some cases, less than 1 mg), PCB model 393B12 (Figure 13), with a sensitivity of 10 V/g and a measurement range of \(\pm 0.5\) g. The sensors were installed on the bridge deck's lower side to evaluate the responses in the vertical direction. In some situations, additional excitation at the lower side of the deck, provided by a non-instrumental hammer, was useful to increase the amplitude of movement of the deck. The accelerometers were distributed along the span in the centre of each track, and considering four more additional accelerometers, two in each external extremity of each deck, and other two in the internal extremity of each half-deck, between the longitudinal expansion joint. All the accelerometers were placed along the embedded steel beams from the deck.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Name** & **No. of Spans** & **L (m)** & **No. of Tracks** & **Max. Speed (km/h)** \\ \hline
1 & Braço do Cortico underpass & 1 & 7.02 & 2 & 160 \\ \hline
2 & Vale da Negra underpass & 1 & 7.10 & 2 & 140 \\ \hline
3 & Casalheira underpass & 1 & 10.92 & 2 & 160 \\ \hline
4 & Canelas bridge & 6 & \(6\times 12.00\) & 2 & 170 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Overview of the filler-beam bridge characteristics.  
Figure 12: Cross sections and views of the decks of the Braco do Cortiço (**a**,**b**), Vale da Negra (**c**,**d**) and Cascalheira (**e**,**f**) underpasses and cross section and view of the first span of the Canelas bridge (**g**,**h**).  
The post-processing of the results of these ambient vibration tests was performed using the Enhanced Frequency Domain Decomposition method (EFDD). This method, which is available in the ARTeMIS(r) software [52], allowed the estimation of the modal parameters of the bridges, particularly, natural frequencies, mode shapes, and damping coefficients, taking into account the peaks of the curves of the average normalized singular values decomposition of the spectral density matrices of the method, which correspond to the vibration modes, as shown in Figure 14.  
Figure 14: Enhanced Frequency Domain Decomposition method (EFDD) curves: average normalized singular values of the spectral density matrices.  
Figure 13: Ambient vibration test typical layout with a detail of the accelerometer PCB 393B12.  
Table 5 presents the results for all the tested bridges, namely, the mode shapes of each vibration mode for all bridges and the corresponding natural frequencies \(f\) and damping coefficients \(\xi\). In some bridges, the EFDD method allowed the detection of three vibration modes, while on other bridges, the method only allowed the detection of two vibration modes.