# Evaluation of Ride Comfort under Vortex-Induced Vibration of Long-Span Bridge
## 4 Result and Discussion
### Drivers' Ride Comfort Evaluation  
#### 4.2.1 OVTV  
Taking a sedan car as an example, assuming that the vortex vibration frequency is 0.328 Hz and the amplitude is 0.3 m, the comfort OVTVs under different road grades and vehicle speeds are calculated, as shown in Figure 8.  
In Figure 8, when the sedan car travels on a bridge without vortex-induced vibration, OVTVs for a Class A road are below 0.315 m/s\({}^{2}\), indicating that drivers experience no discomfort. Conversely, for Class B and C roads, OVTVs exceed 0.315 m/s\({}^{2}\), leading to considerable driver discomfort. However, when vertical bending vortex-induced vibrations occur in the main beam, irrespective of road surface roughness, OVTVs remain below 0.315 m/s\({}^{2}\), ensuring driver comfort. Notably, on A-class roads, vehicle speeds exceeding 45 km/h result in OVTVs surpassing 0.315 m/s\({}^{2}\), causing driver discomfort. This observation confirms that vortex-induced vibration does indeed lead to driving comfort issues. Generally, OVTVs increase with rising vehicle speed and road grade, indicating worsening comfort conditions as both parameters increase. Furthermore, when examining OVTVs under identical road conditions, with and without considering vortex-induced vibration (VIV), it becomes evident that the discrepancy between these two values is negligible. This suggests that the OVTV is not an appropriate metric for assessing driving comfort in the presence of vortex-induced vibration.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Frequency (Hz)** & **Mode** & **Frequency (Hz)** & **Mode** \\ \hline
0.082 & & 0.276 & \\
0.103 & & 0.328 & \\
0.121 & & 0.381 & \\
0.178 & & 0.496 & \\
0.197 & & 0.557 & \\
0.233 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Frequencies of vertical modes of vibration of the bridge.  
Figure 8: Relationship between OVTV and road grade and vehicle speed. (**a**) The comfort value of OVTV calculated without VIV (**b**) The comfort value of OVTV calculated with VIV.  
Figure 9 presents OVTVs for four vehicle types on a Class A road with the speed set at 80 km/h. The pink dashed line indicates the minimum comfort threshold, which is used to distinguish whether discomfort will be felt or not. It also illustrates their relationship with changes in vortex frequency and amplitude. When the amplitude ranges from 0.1 m to 0.5 m and the vortex vibration frequencies are below 0.276 Hz, comfort OVTVs remain below 0.315 m/s\({}^{2}\), signifying driver comfort. However, starting at 0.276 Hz, the OVTV rapidly increases with amplified amplitude and frequency. Simultaneously, the comfort curves of the four vehicle types closely resemble each other, indicating minimal impact of the vehicle type on the OVTV. Overall, the comfort OVTV index rises with increasing vortex vibration amplitude and frequency. Notably, when the frequency ranges from 0.082 to 0.557 Hz and the amplitude remains below 0.1 m, the OVTV shows minimal variation, forming an almost linear trend.  
It is important to highlight that within the 0.25 Hz range, the OVTV remains constant, regardless of vortex vibration frequency and amplitude. This stability arises because the frequency modulation coefficient corresponding to the frequency weighting function is nearly zero within this range. Consequently, the impact of vortex vibration excitation on the OVTV is minimal, while the acceleration response from the road surface dominates. However, when the frequency exceeds 0.25 Hz, the frequency modulation coefficient increases, resulting in a greater influence of eddy vibration-induced responses. Consequently, the OVTV starts to rise with higher vortex vibration frequencies and amplitudes.  
Figure 9: Relationship between OVTV and frequency and amplitude in different vehicles. (**a**) Sedan car (**b**) Light truck. (**c**) Mini van. (**d**) Motor bus.