## 3 Modeling Approach
### Calculation Results and Analysis of Train Dynamic Response  
Considering when trains traversed the 10 \(\times\) 25 m simply supported beam bridge at speeds ranging from 60 to 120 km/h, the train dynamic response characteristics are summarized in Table 5 and further visualized in the line chart presented in Figure 14.  
Figure 14: Cont.  
As shown in the above charts, when the train traversed the bridge at speeds ranging from 60 to 120 km/h, the peak lateral acceleration of the train reached 0.38 m/s\({}^{2}\) under the single/double-track 80 km/h operational condition, complying with the specification requirement of lateral vibration acceleration \(\leq\)1.0 m/s\({}^{2}\). The maximum vertical acceleration of 1.17 m/s\({}^{2}\) occurred at 120 km/h under single/double-track conditions, satisfying the standard requirement of vertical vibration acceleration \(\leq\)1.3 m/s\({}^{2}\). Both the lateral and vertical Sperling indices remained below 2.5 across all speed ranges, indicating \"excellent\" levels of ride comfort in both directions. While train acceleration in both directions demonstrated significant speed dependence, the vertical acceleration exhibited a clear increasing trend with speed, whereas the lateral acceleration showed no distinct speed-related pattern. At identical speeds, the lateral and vertical accelerations showed minimal variation between the leading and middle cars. The vertical ride comfort deteriorated with an increasing speed, while the lateral ride comfort maintained no consistent speed-dependent relationship.  
Figure 14: Dynamic response trend diagrams of train.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Working** \\ **Condition** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Speed of** \\ **Vehicle** \\ **(km/h)** \\ \end{tabular} } & \multicolumn{2}{c}{**Lead Car**} & \multicolumn{4}{c}{**Middle Car**} \\ \cline{3-8}  & & & **Vertical Acceleration** & **Lateral Acceleration** & **Operling Comfort** & **Vertical Acceleration** & **Lateral Acceleration** & **Operling Comfort** \\  & & **(m/s\({}^{2}\))** & **(m/s\({}^{2}\))** & **Horizontal Vertical** & **(m/s\({}^{2}\))** & **acceleration (m/s\({}^{2}\))** & **Horizontal Vertical** \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Single \\ track \\ \end{tabular} } & 60 & 0.52 & 0.28 & 2.01 & 1.75 & 0.53 & 0.28 & 2.01 & 1.76 \\  & 70 & 0.64 & 0.37 & 2.11 & 1.90 & 0.63 & 0.36 & 2.12 & 1.89 \\  & 80 & 0.72 & 0.38 & 2.16  
Influence of Lateral Stiffness Variation of Bridge on Dynamic Response of Maglev Vehicle-Bridge System  
Long-span beam bridges have relatively large spans, and their main girders are prone to significant demode shape under dynamic loads. Particularly for maglev vehicles, which require strict track regularity, such bridges demand higher stiffness requirements. For medium-to-long-span, low-to-medium-speed maglev continuous beam bridges, the lack of established standards and limited reference engineering cases has resulted in no unified stiffness criteria. Evaluating these bridges using the stiffness limits for high-speed maglev bridges would inevitably lead to material waste. Therefore, investigating the stiffness parameters of such bridges is crucial for determining appropriate stiffness values that meet operational requirements.  
For long-span continuous beam bridges, the stiffness of both the main girder and pairs primarily determines the overall structural stiffness. In this study, we adopted a parametric approach by varying the elastic moduli of these components. The elastic modulus was adjusted by \(-50\%\), \(-25\%\), \(\pm 0\%\), \(+25\%\), and \(+50\%\) to modify the corresponding stiffness matrices. Using a maglev vehicle as the study subject, we calculated the wheel-axle dynamic responses at speeds of 60, 70, 80, 90, 100, 110, and 120 km/h under various operating conditions, analyzing how different parameters affected the dynamic wheel-axle responses.