## 4 Numerical Application to Jibuao Bridge  
Jiubao Bridge is one of the ten largest bridges over the Giantang River. Its total length is 1855 m. The main bridge is a continuous composite beam-steel arch bridge, and the approach bridge has a constant section with spans of 85 m. The whole span arrangement is as follows: 55 m + 2 \(\times\) 85 m + 78 m + 21.785 m (northern approach) + 3 \(\times\) 210 m (main bridge). The span layout of Jiubao Bridge is shown in Figure 4a. In this paper, the northern approach bridge was the focus.  
The Jiubao northern approach bridge is a multi-span continuous composite bridge. Its composite girders consist of a concrete deck and steel U-shaped girders. A typical cross section of the Jiubao northern approach bridge is shown in Figure 4b. The characteristic  
Figure 4: The span layout of Jiubao Bridge (m) and the standard section of the northern approach bridge (unit: cm). (**a**) Span layout; (**b**) standard section.  
Figure 3: (**a**) Vertical dynamic mid-span velocity, (**b**) vertical dynamic vehicle velocity, (**c**) vertical dynamic mid-span acceleration, (**d**) vertical dynamic vehicle acceleration, and (**e**) vertical dynamic vehicle displacements.  
cylinder strength of concrete was 32.4 MPa, and the modulus of the concrete was 34.5 GPa. The shear stiffness of the studs was calculated and was equal to 5138.2 MPa. The influence of axial forces of the six post-tensioned tendons on the dynamic response was also included in the numerical analysis. The axial force value of each prestressed tendon applied on the composite beam was 3795.2 kN. The mass of the test vehicle was \(m_{v}\) = 35,000 kg, the stiffness \(k_{v}\) = 11,667 kN/m, the damping ratio \(\xi_{v}\) = 0.2, and the vehicle speed was 10 m/s.  
The vertical displacement and the acceleration at the middle of the second span were subjected to Fourier transform to obtain the spectrogram. As shown in Figure 5, the vibration frequency could be obtained. Figure 6 shows the vertical displacement and acceleration of the vehicle, along with their corresponding spectrograms. Under the influence of the vehicle's driving frequency, multiple bifurcation peaks appeared in the spectrogram. The average value of the bifurcation peaks corresponded to the vibration frequency of the bridge. The comparison results of the frequency spectrum analysis of the vehicle and bridge signals, along with the structural vibration frequency obtained from the natural vibration analysis of the bridge itself, are shown in Table 1. The first four mode shapes of the deflection for the northern approach bridges are shown in Figure 7. These mode shapes were obtained through free vibration analysis.  
Figure 5: Dynamic response of the bridge at the middle of the second span. (**a**) Vertical displacement; (**b**) vertical displacement spectrum; (**c**) acceleration; (**d**) acceleration spectrum.  
Figure 6: Dynamic response of the vehicle. (**a**) Vertical displacement; (**b**) vertical displacement spectrum; (**c**) acceleration; (**d**) acceleration spectrum.  
Figure 7: The first 4 mode shapes of the deflection for the northern approach bridges.  
The influence of the duration of vehicle running time on the indirect identification results was also discussed. With the increasing running time of the vehicle, it is observed in Figure 8 that the peak spacing of the acceleration spectrum remained relatively unchanged, but the peaks gradually became larger and approached a fixed value, and bifurcation occurred at each peak point. Compared to short-term spectrograms, long-term spectrograms were easier to identify, and the frequency identification became clearer as the duration of vehicle running time increased.