# Effect of Vinyl Flooring on the Modal Properties of a Steel Footbridge
## 2 Unexpected High Experimental Damping Ratios of the Jorge Manrique Footbridge
### Experimental Identification of the Modal Parameters of the Jorge Manrique Footbridge  
Subsequently, an AVT was performed to identify experimentally the modal parameters of the structure. The experimental test was conducted under ambient conditions. The response of the structure under ambient excitation was measured along two gridlines located on each lateral edge of the deck (Figure 2). As a data acquisition system, the Kinemetrics Granite equipment was considered. A total of 2 \(\times\) 11 points equally distributed along each longitudinal alignment were instrumented. Three high sensitivity triaxial force balance accelerometers (Kinemetrics Episensor ES-T, Pasadena, US) were used. Two of these devices were established as references, and the other one was moved successively to the different positions of the gridlines. An optimal sensor placement algorithm [24] was used to select the best location for the two reference accelerometers. The considered locations ensure the identification of all the vibration modes whose natural frequencies were inside the range that characterizes the pedestrian-structure interaction phenomenon [13; 14]. Twenty different set-ups were conducted during this AVT. The parameters required to conduct this AVT were determined based on the results of the previous numerical modal analysis. Thus, a sampling frequency of 100 Hz and duration for each set-up of 600 s were considered. In order to identify the experimental modal parameters of the footbridge, the signals recorded during this AVT were processed via an OMA algorithm. The stochastic subspace identification (SSI) method [20] was considered herein due to its greater accuracy for the estimation of the damping ratios of the structure [25]. This identification method is implemented in the software package  
Figure 3: First three numerical, \(\phi_{num,j}\) and experimental, \(\phi_{exp,j}\), vibration modes of the Jorge Manrique footbridge with the vinyl flooring (being \(j\) the number of the considered vibration mode). Artemis [26], which has been used herein. Thus, the first three natural frequencies and associated vibration modes were identified experimentally. Table 1 shows the first three experimental natural frequencies, \(f_{exp,j}\) (being \(j\) the number of the considered vibration mode), and Figure 3 illustrates the first three experimental vibration modes, \(\phi_{exp,j}\), of the Jorge Manrique footbridge. The obtained numerical and experimental natural frequencies and vibration modes are compared in Table 1. In order to validate the correlation between the numerical and experimental modal parameters both the relative differences, \(\Delta f_{exp,j}^{num,j}\), between each considered numerical and experimental natural frequency \(j\) and the modal assurance criterion ratios, \(MAC_{exp,j}^{num,j}\), between each considered numerical and experimental vibration mode \(j\) were analyzed [27]. The relative difference, \(\Delta f_{exp,j}^{num,j}\), between a numerical and experimental natural frequency \(j\) may be expressed as:  
\[\Delta f_{exp,j}^{num,j}=\frac{f_{num,j}-f_{exp,j}}{f_{exp,j}}\Delta 100\ [\%] \tag{1}\]  
where \(f_{num,j}\) is the numerical natural frequency [Hz] and \(f_{exp,j}\) is the experimental natural frequency [Hz] of the vibration mode \(j\). The modal assurance criterion, \(MAC_{exp,j}^{num,j}\), between a numerical and experimental vibration mode \(j\) may be defined as:  
\[MAC_{exp,j}^{num,j}=\frac{(\phi_{num,j}^{T}\Delta\phi_{exp,j})^{2}}{(\phi_{ num,j}^{T}\Delta\phi_{num,j})\Delta(\phi_{exp,j}^{T}\Delta\phi_{exp,j})}\ [-] \tag{2}\]  
where \(\phi_{num,j}\) and \(\phi_{exp,j}\) are respectively the numerical and experimental vibration modes to be compared and \({}^{T}\) denotes the transpose. A good correlation between two vibration modes is achieved when the value of its \(MAC_{exp,j}^{num,j}\) ratio is greater than 0.90 [27]. As Table 1 shows both the value of the experimental natural frequencies and associated vibration modes are in good agreement with the results obtained numerically.