# Possibility of Bridge Inspection through Drive-By Vehicles
## 3 2D VBI Model
### Effect of Damage on Bridge Frequencies  
To compare the effects of different damages on the bridge, 12 damage models shown in Table 1 are analyzed.  
Figure 2: Comparison of mid-point displacements of the 2D vehicle–bridge interaction (VBI) ABAQUS model with the model of [PERSON] et al. [24].  
Three damage factors were simulated in the model: damage location, damage intensity, and damage size. Three different damage locations, damage intensities, and damage sizes were simulated in the model.  
A healthy bridge of the example [24] was simulated first. A time step of 0.001 s was selected to generate adequate data. The time history of the vehicle's vertical acceleration was recorded and shown in Figure 3. Three frequencies are successfully extracted from the Fast Fourier Transform (FFT) analysis of the vehicle's vertical acceleration (Figure 4).  
In the frequency spectrum plot (Figure 4), the bridge frequency is about 4.76 Hz, the vehicle frequency is about 1.48 Hz, and the driving frequency is about 0.04 Hz. The three frequencies match well with the results of [PERSON] et al. [24].  
Based on the validated healthy bridge model, the above-mentioned damage cases are embedded in the model and simulated. Three model cases are created to study the effect of different damage locations, which are at the location of 1, 5, and 10 m from the bridge's left end. The damage was simulated as a 1 m long segment in the bridge with half Young's modulus of other elements. Other properties are kept the same as before. The simulated vertical acceleration data of the vehicle were recorded and used to extract the frequencies. The first frequency of the bridge with damage at 10, 5, and 1 m is 4.6, 4.68, and 4.76 Hz, respectively (Figure 5). The results show that the decrease of bridge frequency has a linear relationship concerning the distance between the support and the damage location. For damages close to the support, the resulted frequency does not change compared to that of the healthy  
A symmetric damage pattern was also simulated. The results show that if the damage location is symmetrical about the mid-span of the bridge. The identified frequency would be the same.  
Another three model cases were created to study the effect of different damage levels. The Young's modulus of a 1 m long segment of the bridge at the 10 m location from the left support is reduced by 20%, 40%, and 60% compared to its original Young's modulus. Young's modulus' nominal variation could reflect the stiffness reduction caused by either section loss or material degradation. The identified first frequency of the bridge is 4.72, 4.64, and 4.52 Hz, respectively.  
Four damage sizes at each damage location were simulated to study the vehicle responses' sensitivity to damage sizes. The damage was still being simulated as only  
Figure 4: Fast Fourier transform of the bridge’s vertical acceleration.  
Figure 5: Fast Fourier transform results in different damage locations.  
having half the Young's modulus as these of other elements. The damage sizes were chosen as 1 m, 50 cm, and 10 cm, respectively.  
At the 1 m damage location, the sensitivity of the damage size is very low. It is apparent that only the amplitude of the frequency spectrum changes, but not the frequency value.  
At the 5 m damage location, the identified bridge frequency for the damaged bridge with a 1 m, 50 cm, and 10 cm length damage is 4.68, 4.72, and 4.76 Hz, respectively. It could be found that the identified bridge frequency reduces as the length of the damage segment increases.  
At the 10 m damage location, the bridge's identified frequency with the 1 m, 50 cm, and 10 cm length damage is 4.6, 4.68, and 4.86 Hz, respectively. A similar trend is found in the case of damage at the 5 m location.