# Dynamic Interaction Analysis of Long-Span Bridges Under Stochastic Traffic and Wind Loads
## 5 Conclusions  
This paper presents a method for a wind-vehicle flow coupled vibration analysis of large-span bridges. The proposed method comprehensively considers the joint effects of wind and vehicle flow loads. It systematically analyzes the dynamic response of bridges under the influence of multiple factors using coupled dynamic models, finite element methods, and nonlinear solution techniques. The key conclusions are as follows:  
1. The study reveals that under sparse traffic conditions, the vertical vibration amplitude of the bridge typically ranges from approximately 0.1 to 0.7 cm, with a peak displacement of 0.78 cm observed during specific time intervals. This indicates that sparse traffic results in lower vibration amplitudes due to the extended intervals between vehicles, leading to reduced vibration accumulation.
2. Under dense traffic conditions, the vertical vibration amplitude increases to a range of 0.3 to 1.5 cm with a maximum recorded displacement of 1.5 cm. Dense traffic conditions amplify the bridge's vibration response by up to 114.28%, highlighting the significant impact of continuous vehicle loads on bridge dynamics.
3. The analysis indicates that wind loads exert a negligible effect on the vertical displacements of the bridge while significantly influencing its lateral displacements. Wind loads introduce an additional force that affects the bridge's horizontal vibration, especially under conditions of dense traffic and high wind speeds. Under such conditions, the maximum lateral displacement of the bridge induced by wind loads can reach up to 2 cm.  
In future work, several limitations identified in the current study will be addressed. Plans are to refine the linear vehicle model to better capture real-world vehicle dynamics, incorporate additional environmental factors such as temperature and seismic loads, and consider heterogeneous pavement properties to more accurately represent vehicle-bridge structure interaction. Aeroelastic nonlinearity will also be incorporated through coupled aeroelastic analysis and nonlinear aerodynamic models to account for complex wind-bridge structure interactions. Furthermore, a detailed modal analysis will be conducted to determine the bridge's natural frequencies and modal shapes, which are crucial for a comprehensive understanding of its dynamic response. These improvements will enhance analysis accuracy and reliability, providing a more comprehensive basis for bridge safety assessment and maintenance.  
Software, D.G.; Validation, L.L.; Formal analysis, J.W.; Investigation, Y.H.; Writing--original draft, R.W.; Writing--review & editing, Y.Q.; Supervision, S.G.; Funding acquisition, R.W. & P.X. All authors have read and agreed to the published version of the manuscript.  
The funding is supported by the National College Students Innovation Training Program. (project no. S202410536059) and the Hunan Provincial \"100-Talent Plan\" Research Fund and Central South University Pre-research Fund (project no. 820180914).  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.  
Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.