## 4 Dynamic Measurements of the Railway Bridge and Crossing Train
### Dynamic Measurements of Selected Steel Bridge  
Forced vibration tests were carried out to identify the natural frequencies, corresponding mode shapes, and damping ratios of the considered railway bridge. Therefore, two  
Figure 12: Single-track steel deck bridge with orthotropic plate selected for in situ measurements. electrodynamic long-stroke shakers, SH1 and SH2, were fastened at the center of the longitudinal main girders beneath the bridge using a stiff hanging construction (see Figure 13). The installed long-stroke shakers have a static mass of around 70 kg and an additional vertical moving mass of 30.6 kg each. Depending on the excitation frequency, excitation force amplitudes up to 440 N for each of the electrodynamic shakers can be applied to the bridge structure. A closed-loop control system enables a constant force amplitude over the entire excitation frequency range of interest, and it is possible to synchronize and operate with several shakers at the same time. Additionally, the asynchronous operation of the two installed long-stroke shakers allows the identification of torsional vibration modes of the considered bridge. Using these shakers ensures the ability to reproduce the measurement results, and a high accuracy is achievable. For this specific measurement, the shakers were fastened hanging on the bottom flange of the main girders. In order to measure the vibration response of the harmonic force-excited bridge, several accelerometers were installed in different locations of the main girders. The sensor and shaker positions are shown in Figure 14.  
Figure 15 illustrates the measured amplitude-frequency response function, evaluated from the executed continuous frequency sweep from 2 to 12 Hz, with a sweeping speed of 2 Hz/min and a constant excitation force amplitude of \(F_{0}\) = 428 N of the two installed synchronized shakers. Three peaks can be detected in the gained frequency spectrum at 3.85 Hz, 4.52 Hz, and 5.51 Hz. The highest peak with a frequency of \(n_{d,1}\) = 4.52 Hz corresponds to the first bending mode of the bridge where the two main girders exhibit a vibration response in phase with more or less the same size of dynamic displacement, and it is evaluated as most critical regarding train-induced resonance vibrations. Hence, the later applied vehicle-based iSHM method focuses on identifying this most relevant bridge's natural frequency. Figure 14: Positions of the two installed electrodynamic long-stroke shakers and of the installed accelerometers A1–A6 at the bottom side of the bridge’s longitudinal main girders. Figure 13: Two electrodynamic long-stroke shakers, SH1 and SH2, fastened at the center of the longitudinal main girders beneath the bridge. The two detected additional frequencies at 3.85 Hz and 5.51 Hz correspond to local vibration modes of the longitudinal main girders 1 and 2; see Figure 14. The outer main girder 1 supports the cantilever steel construction, and hence, its frequency and vibration amplitude are lower than the frequency of the inner main girder 2 (cf. Figure 15). This interesting finding of two local vibration modes is a bridge-specific characteristic that must be considered during the measurement data analysis and interpretation. The damping ratio \(\zeta\) of the bridge's most relevant first bending mode is determined by applying the half-power bandwidth method to the acceleration amplitude frequency response function in Figure 15 and results in \(\zeta\) = 1.88% as a mean value out of five repeatedly conducted measurements with the same test setup. Thereby, the standard deviation of the measured damping ratios is determined by \(\sigma\) = 0.012%, which is very small and confirms the advantage of the applied forced vibration testing method. In addition to the synchronous sweep, an asynchronous sweep was executed with a sweeping speed of 2 Hz/min and a constant excitation force amplitude of \(F_{0}\) = 214 N per shaker.