## 4 Dynamic Measurements of the Railway Bridge and Crossing Train
### Dynamic Measurements of Crossing Train
It should be noted that the sensors installed on the considered steel bridge remained installed according to the positions shown in Figure 14; thus, both the vehicle and bridge vibration responses were measured during the train crossing events and analyzed in this section. Figure 18a illustrates the relevant low-pass filtered time-history section of the measured forced vibration response of bogie frame \(b2\) for accelerometer a213 during the train crossing event. Figure 18b shows the corresponding frequency response function calculated by FFT. Therefore, the filter cut-off frequency was chosen as 10 Hz. In addition, Figure 18c,d shows the measured vibration response of the car body \(c1\) for accelerometers a333 and the corresponding FFT result. In this measurement, the train run was executed with the Salzburg driving direction at 135 km/h (=37.5 m/s), and hence, the considered bogie \(b2\) arrived as the second to last bogie on the steel bridge (see Figure 17). Figure 18: Measured vibration responses of bogie frame \(b2\) and car body \(c1\) during train crossing with a speed of 135 km/h: (**a**) time history of sensor a213; (**b**) corresponding FFT result of sensor a213; (**c**) time history of sensor a333; (**d**) corresponding FFT result of sensor a333. In relation to the bridge span length of 33.3 m, the duration of the bogie crossing at 135 km/h is just around 1 s, and hence, selecting the relevant time section for calculating the corresponding frequency spectra is essential. It is seen from the FFT result of the vibration response of the bogie frame \(b2\) (Figure 18b) that the bridge's natural frequency, which was already determined by the forced vibrations tests (cf. measured value \(n_{d,1}=4.52\) Hz, see Section 4.2)--can be identified at \(n_{d,1,T1}=4.38\) Hz and this train-identified frequency agrees quite good with the result of the dynamic bridge measurements. The slight difference of around 3% between the in situ measured and train-identified first bending frequency is attributed to the vehicle-bridge-interaction effect, in particular, the unsprung train-mass-induced frequency shift (cf. Section 3.2). The additional peaks that are visible in the frequency response function of Figure 18b correspond most likely to excited resonance frequencies of the bogie, which obviously also occur in the frequency spectra (cf. calculated bogie frequencies in Section 3.2). The frequency response function given in Figure 18d, calculated from the vibration response of the car body \(c1\), does not allow the identification of the bridge's natural frequency. It is assumed that the dominant visible frequency of 1.34 Hz corresponds to the low vertical vibration mode of the car body, which is also evident in a similar form (at 0.9 to 1.9 Hz) in the analysis of the numerically derived vibration response of the car bodies (see Figure 5 in Section 3.2). To prove that the selected train-identified frequency peak of \(n_{d,1,T1}=4.38\) Hz in Figure 18b corresponds to the first bending frequency of the considered steel bridge, the measured acceleration response of the considered steel bridge during train crossing at 135 km/h is illustrated in Figure 19a for sensor A2 in the time-domain. In addition, Figure 19b shows the FFT result of the time decay function after the train has completely left the bridge. It is noted that the displayed acceleration signal of the sensor A2 has been low-pass filtered with a cut-off frequency of 20 Hz. Figure 19: In situ measured acceleration response of the considered steel bridge during train crossing at 135 km/h: (**a**) time-history; (**b**) FFT result of time decay function after the train left the bridge. It is seen from the FFT result of the time decay function in Figure 19b that the highest frequency peak occurs at 4.38 Hz, which is close to the bridge's first bending frequency \(n_{d,1}=4.52\) Hz determined via forced vibration tests (see Figure 15). This indicates that the first bending mode of the bridge is dominantly excited during the train crossing event.