## 5 Field Experiments
The focus of the present research is the variation in the frequency difference between the fundamental natural frequency and the frequency of the forced vehicle excitation among different vehicle speed cases, which is not significantly influenced by the velocity and mass weight of the vehicles based on the above. Therefore, the role of the velocity and mass weight of the vehicles does not have to be removed from the plots given in Figures 17 and 18 to arrive at the near-to-exact natural frequencies of the bridge structure for the required study to take place. In addition, in Table 3, the frequencies of the forced vehicle excitation identified for different cases vary in a wide range (2.9-4.0 Hz). This suggests that with sufficient road surface roughness (the variation range of the road surface of the actual Renyihe Bridge is \(-\)0.025 to 0.025 m according to Ref. [20]), the nature of the vehicle excitation changes in accordance with the vehicle speed variation. Comparing the 20 km/h vehicle speed case with the 30 km/h vehicle speed case, it can be observed that with the decrease in vehicle speed, the frequency of the vehicle excitation markedly decreases and becomes closer to the low-order natural frequencies of the bridge (the differences between the first-order natural frequencies and the frequencies of the forced vehicle excitation for different cases shown in Figure 19 clearly demonstrate this). Therefore, stronger structural resonances ought to be excited by the passing vehicles when the vehicle speed is reduced. This observation can well answer the question posed in Section 4.3, i.e., why the resonant response is more significantly amplified for a lower vehicle speed case after the road surface roughness is increased. However, by comparing the 20/30 km/h vehicle speed case with the 40/50 km/h vehicle speed case in Figure 19, a different observation is noted; i.e., the frequency difference increases with the decrease in vehicle speed. According to the literature, the energy distribution of the vehicle excitation in the frequency range (2.85-11.8 Hz) depends on both the road surface roughness and the automobile engine frequency. For the smooth road surface case, the energy distribution totally depends on the automobile engine frequency. According to Figure 10, when the vehicle speed is increased, the energy of the vehicle excitation noticeably shifts to the low-frequency range, suggesting that the automobile engine frequency is decreased. Therefore, for the rough road surface case (the actual Renyihe Bridge), although the nature of the vehicle excitation is influenced due to the effects of road surface roughness when the vehicle speed is decreased, this influence is sometimes not sufficient to bring about the reduction in frequency of the vehicle excitation, as the automobile engine frequency is markedly increased. Moreover, strain sensors were arranged at the bottom on the mid-span cross-section of the fourth main span. These sensors were utilized to measure the maximum structural responses of Renyihe Bridge subject to the passing vehicles. The maximum dynamic stresses so obtained in different vehicle speed scenarios are shown in Figure 20. The data presented in Figure 20 agree well with the results presented in Figure 15 for Cases 7-9. The maximum tensile stresses measured on location are comparable to the tensile strength of the material for all vehicle speed cases, suggesting that structural damages could be induced for all cases. Figure 16: Vehicles employed for field experiments.