## 2 Prediction Model of Acoustic Radiation from SSSFSTs on a Bridge  
The dynamical equations of the URT system can be expressed as follows:  
\[M\ddot{u}+C\dot{u}+Ku=R \tag{1}\]  
where \(M\), \(C\), and \(K\) are the mass, damping, and stiffness matrices; and \(\ddot{u}\), \(\dot{u}\), \(u\) and \(R\) are the acceleration, velocity, displacement, and generalized load vectors, respectively. When applied to the vehicle subsystem, track subsystem, and bridge subsystem, respectively, they can describe the motion state of each subsystem of the elevated railways. The vehicle-track-bridge interaction schematic is shown in Figure 1. The theory used here has been widely used in practical engineering problems [37; 38].  
This paper took an elevated BGB with SSFST for URT as the research object, in which the vehicle model adopted the Type A subway vehicle and established a 35-degree-of-freedom multi-rigid body dynamics model. The dynamic parameters of the Type A subway vehicle can be seen in the literature [18]. The SSFSTs used the 3D finite element model, in which a total of four SSSFSTs were laid on the bridge. The 24 m BGB was simplified as a thin-shell structure to reduce the computational burden. The finite element model did not consider the bridge pier. According to the actual position of the pier, simply supported constraints were applied to the bottom plate of the box-g  
Figure 1: Vehicle-track-bridge dynamic interaction model.  
model, the element size of beam 188 of the rail was 0.05 m, and the 3D element size of the SSSFSTs was 0.3/0.1/0.1 m for length/width/thickness. The finite element model of the SSFSTs-BGB system and the dynamic parameters can be seen in Figures 2 and 3, and Table 1. The excitation was the sixth-grade track irregularity PSD of the US Federal Railroad Administration. The wheel-rail interaction force was calculated using the display integration method proposed by academic [PERSON] [39], and the above wheel-rail force was applied to the finite element model of the line infrastructure as a moving load to solve for its dynamic response. The obtained results were able to provide accurate acoustic boundary conditions for subsequent acoustic solutions.  
The acoustic boundary element method [41] was used to calculate the acoustic radiation of the floating-slabs. The application of the acoustic boundary element method in predicting low-frequency acoustic radiation from structures has been widely recognized for its accuracy and effectiveness. For the acoustic boundary element method, based on the acoustic wave equation, Sommerfeld radiation condition, and Neumann boundary condition Meanwhile, the following basic assumptions are made in the calculation of the acoustic  
Figure 3: The label for SSSFSTs on the bridge.  
Figure 2: The SSSFSTs are on the bridge and finite element models.  
radiation of floating-slabs: The propagation medium is ideal; the air has no reaction force on the floating-slab plate; the floating-slab is the only sound source; the sound waves of the floating-slab are unaffected by the surrounding buildings; the sound waves have no interference effect in propagating; and structural noise is steady-state analysis.