## 2 Two kinds of Top Plate Thickening Low-Acoustic Radiation Bridge Design Scheme  
Elevated high-speed railway bridges are the most common kind, and usually feature 32 m simple-supported concrete BGBs, so this bridge type has been selected as the object of study in this paper. Recent research results have shown that the top plate overwhelmingly determines the amount of overall noise radiated by BGBs [37; 38; 39], and thickening the whole top plate can reduce its acoustic radiation, making it a good design solution for low-acoustic radiation bridge types [23; 24]. When a train passes through an elevated bridge, due to the contact between the wheels and the rails, the vibrational energy is transferred to the bridge through the rail structure, which causes the bridge to vibrate and radiate noise. As such, the vibrational energy generated by wheel-rail interaction is first transferred to the point of contact between the rail and the bridge deck. According to the requirements of the specific project, local thickening can be applied to the point of contact of the BGB and the rail to reduce the radiation noise of the BGB [25]. This design solution not only reduces the weight of the bridge, but also reduces costs by using prefabricated bridge components, compared to the process of thickening the top plate of the BGB.  
According to the literature [11], the main reason for the radiation of soundwaves from the BGB is related to the resonance effect, its own modal acoustic radiation efficiency, and the violent vibration resulting from external excitation. The bridge type influences all of the above factors, especially the resonance effect and the modal acoustic radiation efficiency, both of which are most closely related to the BGB type. Therefore, the authors consider the following objectives when carrying out the design of a BGB with a thickened top plate in terms of noise control:  
1. The design of the thickened BGB top plate can enhance key parameters, such as the bending stiffness of the BGB, and thus reduce its vibrational response;
2. The top plate of the BGB is the most important component contributing to its acoustic radiation, and local vibration within it significantly affects its acoustic radiation. Thickening the top plate can change the overall vibrational distribution of the BGB, especially in cases of the partial thickening of the top plate, which will not have a uniform thickness, and this has a stronger impact on the vibrational distribution. Resonance at certain frequencies can be avoided to a certain extent, and the change in vibrational pattern can affect the modal acoustic radiation efficiency of the BGB, thus weakening its acoustic radiation capacity.  
In summary, this paper explores the key issues involved in designing bridge plate thickening as it relates to noise reduction by comparing and analyzing the acoustic vibrational characteristics of the initial BGB, the BGB with its whole top plate thickened, and the BGB with under-rail local thickening. The thicknesses of the top plates in both designs are twice that of the initial BGB, and the remaining parameters are kept the same. The initial BGB and the designs with top plate thickening are shown in Figure 1.