# Effect of Vinyl Flooring on the Modal Properties of a Steel Footbridge
## 4 Assessment of the Dynamic Behavior of a Laboratory Footbridge without and with the Vinyl Flooring
### Experimental Identification of the Modal Parameters of the Laboratory Footbridge  
Later, the modal parameters of the laboratory footbridge without and with the vinyl flooring were identified experimentally via the signal processing of the records obtained during the development of two independent AVTs. Both experimental tests were conducted under ambient conditions, where the laboratory footbridge without and with the vinyl flooring was only excited by ambient noise. The response of the structure under these conditions was measured along two gridlines located at the two longitudinal beams of the deck (Figure 4). A total of 2 \(\times\) 5 points equally distributed along each longitudinal beam were instrumented. The previously mentioned three high sensitivity triaxial force balance accelerometers (Kinemetrics Episensor ES-T, Pasadena, United States) and the Kinemetric Granite data acquisition system were used again. The accelerometers were connected to the structure via three screws. Two of these accelerometers were fixed 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. Thus, the considered locations ensure the experimental identification of the first five vibration modes of the laboratory footbridge. Eight different set-ups were conducted during each AVT. A sampling frequency of 100 Hz and duration for each set-up of 600 s were considered for both experimental tests.  
The experimental modal parameters of the footbridge were obtained via the signal processing of the records obtained during the development of each mentioned AVT. An OMA algorithm in time domain, the SSI algorithm [20] was used for this purpose as implemented in the software Artemis [26].  
Figure 7 illustrates the singular values decomposition of the spectral densities for all the test set-ups and the experimental natural frequencies of the laboratory footbridge without and with the vinyl flooring according to the SSI algorithm [20].  
Figure 7: _Cont._Thus, the first five natural frequencies of the laboratory footbridge without, \(f^{wo\_pf}_{exp,j}\), and with, \(f^{w\_pf}_{exp,j}\), the vinyl flooring (being \(j\) the number of the considered vibration mode), and the associated vibration modes, \(\phi^{wo\_pf}_{exp,j}\), and \(\phi^{w\_pf}_{exp,j}\), were identified experimentally. Table 3 shows the first five experimental natural frequencies, \(f^{wo\_pf}_{exp,j}\) and \(f^{w\_pf}_{exp,j}\), and Figures 5 and 6 illustrate the first five experimental vibration modes of the laboratory footbridge, \(\phi^{wo\_pf}_{exp,j}\) and \(\phi^{w\_pf}_{exp,j}\).  
Finally, the numerical and experimental natural frequencies and vibration modes of the laboratory footbridge without and with the vinyl flooring have been compared in Table 3. In order to validate the correlation between the numerical and experimental modal parameters both the relative differences, \(\Delta f^{wo\_pf}_{j}\) and \(\Delta f^{w\_pf}_{j}\) (being \(j\) the considered vibration mode), and the modal assurance criterion ratios, \(MAC^{wo\_pf}_{j}\) and \(MAC^{w\_pf}_{j}\), have been taken into account again. As Table 3 shows both the value of the experimental natural frequencies and associated vibration modes are in good agreement with the results obtained numerically. All the relative differences, \(\Delta f^{wo\_pf}_{j}\) and \(\Delta f^{w\_pf}_{j}\), are lower than 10% and all the \(MAC\) ratios, \(MAC^{wo\_pf}_{j}\) and \(MAC^{w\_pf}_{j}\), are greater than 0.90.