# Evaluation of Ride Comfort under Vortex-Induced Vibration of Long-Span Bridge
## 1 Introduction
[19] analyzed the influence of vibration inside the train on ride comfort when the train passed a railway bridge under crosswind conditions, taking into account factors such as wind load, track conditions, speed, and the lateral vibration of the bridge, using the average and continuous comfort index in the European standard EN12299 [20] and the Sperling index in the Chinese standard GB/T5599-2019 [21], for evaluation and comparing the difference between the two standards. [PERSON] et al. [22] developed a dynamic system for wind-suspended monorail bridges. They introduced a method for accurately simulating aerodynamic wind forces on both the bridge and moving vehicles. Additionally, they investigated how turbulent crosswinds impact the bridge's dynamic response and passenger comfort during vehicle travel. The findings indicate that turbulent crosswinds significantly affect the dynamic performance of the suspended monorail axle system. Passengers may experience discomfort when the vehicle traverses the bridge during strong turbulent crosswinds. [PERSON] et al. [23] assessed the dynamic performance of a steel arch bridge in Portugal under light rail traffic loads. They employed moving load models and vehicle-bridge interaction models to evaluate not only traffic safety but also passenger and pedestrian comfort. However, few studies have considered the impact of whole-body vibrations on drivers and passengers under vortex-induced vibration. [PERSON] et al. [24] devised a wind-vehicle-bridge coupling system tailored for assessing ride comfort during vortex-induced vibration, employing the ISO 2631-1:1997 standard [14]. Their findings suggest that as the number of vehicles on the bridge increases, the consideration of additional mass and damping from the vehicle-axle system leads to a reduction in the dynamic response OVTV of the vehicles. Concurrently, the study investigates how ride comfort is affected by factors such as vehicle speed, vehicle type, road roughness, and the number of vehicles. [PERSON] et al. [25], following ISO 2631-1 [14] guidelines, introduced a comfort evaluation program for long-span bridges exposed to traffic flow during vortex-induced vibration. The wind-vehicle-bridge coupling analysis took into account the complex interactions among these components and employed the comfort index OVTV to assess how varying traffic densities, proportions, and road roughness impact driving comfort on the Yingwuzhou Bridge during vortex vibration events. [PERSON] et al. [26] developed a coupled eddy current-vehicle-bridge system tailored for addressing the multi-mode locking region observed in long-span suspension bridges. Adhering to ISO 2631-1 standards [14], the study examined the driving comfort index OVTV for three vehicles exposed to eddy vibrations and investigated wheel bouncing behavior that could occur in adverse road conditions and high-order eddy vibrations. Previous research has predominantly concentrated on evaluating driving comfort using the OVTV index, while relatively limited attention has been given to the MSI index as outlined in ISO2631-1:1997 [14]. The novelty of this article lies in providing a convenient method for evaluating ride comfort under vortex-induced vibrations. 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 driving comfort after vortex-induced vibration occurs on a bridge. Simultaneously, it explores the MSI index, which has been overlooked by previous researchers, showcasing a new perspective for assessing ride comfort under vortex-induced vibrations, namely the MSI index. The objective of this study is to assess the ride comfort of vehicles encountering vertical bending vortex-induced vibrations on extended bridges. Vehicle models, accompanied by four-wheel road surface random excitation and wheel excitation input models during vortex-induced vibration, were developed to analyze the dynamic responses of individual vehicles under these conditions.