# Evaluation of Ride Comfort under Vortex-Induced Vibration of Long-Span Bridge
## 5 Conclusions  
This study introduces a road-bridge-vehicle vibration model and a rapid evaluation method to assess vehicle comfort during vortex-induced vibration on long-span bridges. The method offers the benefits of straightforward modeling and rapid calculations while avoiding complex finite element modeling and iterative solving. It can simply and quickly evaluate the driving comfort after vortex-induced vibration occurs on the bridge. The study analyses the impact of various parameters on the OVTV and MSI, including vehicle speed, road grade, vortex-induced vibration frequency, and amplitude. It establishes a reference limit value for vortex-induced vibration amplitude based on the OVTV and MSI values. Conclusions are drawn based on the study's findings. * Vortex-induced vibration significantly impacts driving comfort. Generally, as vehicle speed and road grade increase, the OVTV rises, suggesting a decline in comfort. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Frequency (Hz)** & **MSI (\%)** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline
0.082 & 2.18 & 4.38 & 6.58 & 8.78 & 10.98 & 13.18 & 15.38 & 17.58 & 19.78 & 21.98 \\
0.103 & 1.22 & 2.45 & 3.67 & 4.90 & 6.12 & 7.35 & 8.58 & 9.80 & 11.03 & 12.25 \\
0.121 & 0.59 & 1.17 & 1.76 & 2.35 & 2.94 & 3.53 & 4.12 & 4.70 & 5.29 & 5.88 \\
0.178 & 0.22 & 0.44 & 0.66 & 0.88 & 1.10 & 1.32 & 1.54 & 1.76 & 1.98 & 2.21 \\
0.197 & 0.22 & 0.44 & 0.67 & 0.89 & 1.11 & 1.33 & 1.55 & 1.78 & 2.00 & 2.22 \\
0.233 & 0.16 & 0.31 & 0.47 & 0.62 & 0.78 & 0.94 & 1.09 & 1.25 & 1.41 & 1.56 \\
0.276 & 0.12 & 0.24 & 0.36 & 0.48 & 0.60 & 0.72 & 0.84 & 0.96 & 1.08 & 1.20 \\
0.328 & 0.10 & 0.19 & 0.29 & 0.39 & 0.49 & 0.58 & 0.68 & 0.78 & 0.87 & 0.97 \\
0.381 & 0.09 & 0.19 & 0.28 & 0.38 & 0.47 & 0.56 & 0.66 & 0.75 & 0.85 & 0.94 \\
0.496 & 0.09 & 0.17 & 0.26 & 0.34 & 0.43 & 0.51 & 0.60 & 0.68 & 0.77 & 0.86 \\
0.557 & 0.12 & 0.24 & 0.36 & 0.48 & 0.60 & 0.71 & 0.83 & 0.95 & 1.07 & 1.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Vortex-induced vibration limit based on MSI (unit: m). Figure 12: Vortex-induced vibration limit based on OVTV and MSI. (**a**) Vortex-induced vibration limit based on OVTV. (**b**) Vortex-induced vibration limit based on MSI. At vortex vibration frequencies below 0.276 Hz, the OVTV stays under 0.315 m/s2, indicating no discomfort for drivers. However, beyond 0.276 Hz, OVTV increases rapidly with amplitude and frequency. Moreover, the comfort curves for all four vehicles are nearly identical, suggesting vehicle type has little impact on OVTVs. * The MSI value increases with amplitude, a result of enhanced acceleration response. Additionally, as frequency rises, the MSI value initially increases but later decreases. This trend links to the frequency modulation coefficient associated with the frequency-weighting function \(W_{f}\), which initially increases and then decreases within the range of 0-0.5 Hz. Importantly, the peak MSI value occurs within the 0.3-0.5 Hz vortex vibration frequency range. This suggests more motion sickness in individuals exposed to high-order vortex vibrations. * Under the same road conditions, with or without considering VIV, OVTVs show minimal difference. However, MSI values vary significantly. This suggests that MSI is better suited than the OVTV to gauge driving comfort in the presence of vortex-induced vibrations. Since vortex-induced vibrations mainly occur at low wind speeds, this study omits wind influence on vehicles. However, it is worth noting that some bridges often experience strong winds during high-order vortex-induced vibrations. Therefore, future research should investigate the impact of strong winds on driving comfort and safety under high-order VIVs. Additionally, it is important to mention that the Motion Sickness Incidence (MSI) index in the ISO 2631-1 standard [14] does not specify a comfort threshold. As a result, comfort evaluation on Motion Sickness Incidence currently relies on qualitative methods.