## 3 Theoretical Model Verification  
### Comparative Verification of Dynamic Calculation Models  
The SSSFSTs two-line BGB was selected as the research object. The acceleration response of the floating-slab vertical vibration was calculated using UM multi-body system dynamics simulation software 9.1 and compared with this paper's model to verify its accuracy. The parameters of various sub-models used in UM demonstrate consistency with the parameters of this paper's model. The vehicle's operating speed was 80 km/h. The coupled vehicle-track-bridge dynamics model established in the UM software and the solution process are shown in Figure 4.  
The vertical dynamics of the track structure were the main influencing factor in its acoustic radiation; therefore, the vertical vibration acceleration response at the center of the \begin{table}
\begin{tabular}{c c c c} \hline
**Track Component** & **Unit Type** & **Dynamical Parameters** & **Value** \\ \hline Rail & Beam188 & \begin{tabular}{c} Elastic modulus (GPa) \\ Poisson ratio \\ Density (kg/m\({}^{3}\)) \\ \end{tabular} & \begin{tabular}{c} 210 \\ 0.3 \\ 7830 \\ \end{tabular} \\ \hline Fastener & Combin14 & \begin{tabular}{c} Stiffness (kN/mm) \\ Damping (Ns/m) \\ Distance (m) \\ \end{tabular} & \begin{tabular}{c} 60 \\ 7500 \\ 0.625 \\ \end{tabular} \\ \hline Floating-slab & Solid45 & \begin{tabular}{c} Slab length (m) \\ Slab width (m) \\ Slab thickness (m) \\ Elastic modulus (GPa) \\ Poisson ratio \\ Density (kg/m\({}^{3}\)) \\ \end{tabular} & \begin{tabular}{c} 6.3 \\ 2.7 \\ 0.25 \\ 0.250 \\ \end{tabular} \\ \hline Steel-spring & Combin14 & \begin{tabular}{c} Stiffness (kN/mm) \\ Damping (Ns/m) \\ Distance (m) \\ \end{tabular} & \begin{tabular}{c} 2.0 \\ 25000 \\ 0.625 \\ \end{tabular} \\ \hline Bridge & Shell63 & \
\begin{tabular}{c} Elastic modulus (GPa) \\ Poisson ratio \\ Density (kg/m\({}^{3}\)) \\ \end{tabular} &
\begin{tabular}{c} 38 \\ 0.2 \\ 2500 \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 1: Element types and dynamic parameters of the track-bridge finite model [34; 40]. Figure 4: Dynamics model of UM dynamic simulation software and solution process diagram: (**a**) UM vehicle-track-bridge dynamics model; (**b**) vehicle-track-bridge dynamics calculation process in UM. second floating-slab on the bridge was chosen for comparison in this paper. A comparison of the vertical vibration acceleration at the center of the second floating-slab, calculated using UM dynamics simulation software and the model in this paper, is shown in Figure 5.  
As shown in Figure 5, the acceleration response of the floating-slab vertical vibration obtained by the two methods was in good agreement. The waveforms were consistent, and the vibration time range and amplitude were also in agreement. This shows that the dynamics model established in this paper can solve the dynamics of the track system. In terms of accuracy, it can be used as an input for acoustic calculations and provides reliable acoustic boundary conditions. Discussion of the Vibration Reduction Track Noise Test Problem and the Verification of Theoretical Methods  
More noise sources are formed when the train passes the bridge, including wheel-track noise, aerodynamic noise, collector system noise, track and bridge structure noise, train vibration noise, etc. When testing the structure noise of a track on a bridge, the acoustic radiation of different sources will affect each other, and the tests also need to avoid the interference of background noise. The structural noise of a ballastless track and that of a bridge have similar frequency ranges; therefore, it is difficult to obtain acoustic radiation test information for an SSFST on the bridge. In addition, the selection of acoustic test point locations on the track structure is affected by acoustic effects during propagation as well as the influence of the various noise source signals. Therefore, it is difficult to test the structural noise of the ballastless track in the field.