## 6 Conclusions  
This study investigates a 10 \(\times\) 25 m simply supported rail beam bridge using proprietary computational software to analyze its natural vibration characteristics and vehicle  
Figure 16: Dynamic response trend diagrams of train. bridge coupled dynamics. The research specifically examines how pier top lateral stiffness influences the dynamic behavior of medium-low-speed maglev train-bridge systems through comprehensive spatial dynamic response calculations under various operational scenarios. The principal findings are as follows:  
1. The dynamic analysis of the 10 \(\times\) 25 m simply supported beam bridge under various operating conditions shows that the lateral displacement of the main girder, lateral displacement and acceleration of the pier top, and lateral and vertical angle of beam end have little correlation with train speed (60-120 km/h) and show no clear pattern under single- or double-track conditions. However, the vertical displacement is significantly affected by track configuration, with the main girder's vertical displacement being notably greater under double-track conditions compared to single-track conditions, while remaining largely unaffected by speed variations and showing no distinct regularity. 2. The pier top lateral stiffness exhibits a significant influence on the bridge's dynamic characteristics. The lateral bending fundamental frequency increases progressively with stiffness enhancement, showing 61.8% growth when the lateral stiffness varies from \(-\)50% to +50%. Conversely, the longitudinal floating fundamental frequency decreases gradually, with a 29.2% reduction over the same stiffness variation range. These variations occur while the vertical linear stiffness at the control pier top remains constant throughout the analysis. Given the pronounced sensitivity of dynamic frequencies to lateral stiffness, precise stiffness control during construction is critical. While a higher lateral stiffness enhances transverse vibration resistance, its detrimental impact on longitudinal performance necessitates a balanced design approach, particularly in wind-prone regions, to mitigate resonance risks. These findings highlight the importance of early-stage parametric stiffness optimization to ensure structural safety and performance. 3. The pier top lateral linear stiffness significantly affects the following three key structural responses: the lateral displacement of the main girder, the lateral displacement of the pier top, and the lateral angle of beam end. As the lateral stiffness increases from \(-\)50% to +50% while maintaining a constant vertical linear stiffness at the control pier top, these responses demonstrate substantial reductions: a 63.2% decrease in main girder lateral displacement, a 60.3% decrease in pier top lateral displacement, and a 55% decrease in the angle of beam end. 4. Within the \(\pm\)50% variation range of pier top lateral stiffness, the study reveals the following three key findings: the lateral vibration acceleration of the main girder shows no monotonic relationship with the pier top linear stiffness; the vertical vibration acceleration of the main girder remains relatively stable, with insignificant variations; and both transverse and vertical vibration accelerations exhibit minimal changes overall. Furthermore, the pier top lateral line stiffness demonstrates a negligible influence on the train's lateral and vertical vibration accelerations. 5. According to the research findings, the pier top lateral stiffness has an insignificant impact on the lateral vibration acceleration of the main girder and also exerts minimal influence on the lateral and vertical vibration accelerations of the train. Therefore, in the process of code revision, it is advisable to consider relaxing the restrictions on the main girder's vibration acceleration caused by variations in pier top lateral stiffness.