## 6 Conclusions  
Based on the train-track-bridge interaction and acoustic boundary element theories, this study compared and analyzed the vibration and noise reduction effects of two design schemes involving thickening the top plate of a BGB. The relevant mechanisms and influencing factors of the design schemes were systematically analyzed. The main conclusions are as follows:  
1. When designing a low-acoustic-radiation BGB, it is recommended to first focus on changing its vibration distribution. Thickening the top plate of the BGB can significantly change its vibration distribution--not only do the self-oscillation characteristics change significantly, but the vibrational frequency of similar vibration characteristics caused by external excitation will be shifted to the weaker frequency band of the initial BGB's acoustic radiation. This evades the resonance effect caused by the small vibration resulting from the peak of acoustic radiation, and weakens the acoustic radiation efficiency of the BGB, thus reducing its acoustic radiation capacity. This will effectively reduce the acoustic radiation performance of a BGB in the lower frequency band;
2. Regarding the sound radiation, compared with the initial BGB, the two noise reduction schemes can limit the sound radiation to the weaker frequency band of the initial BGB, although the designs enhance the sound radiation characteristics and expand its range in this frequency band. Regarding the sound radiation in BGBs induced by severe vibration, compared to small vibration, it is entirely possible to achieve noise reduction by reducing vibration, and the implementation of noise reduction control measures is also easier under this approach. Therefore, thickening the top plate is a good solution for achieving low-sound-radiating BGBs, and the two design solutions  
Figure 14: Acoustic vibration characteristics of BGBs at 27.1 Hz under the three case conditions (unit of vibration: m/s\({}^{2}\)). Figure 15: Correspondence diagram of vibrational acoustic radiation of the BGB at 85.7 Hz under the three working conditions. involving top plate thickening described in this paper can contribute effectively to vibration and noise reduction;
3. Regarding the acoustic radiation characteristics of BGBs related to small-amplitude vibration in the lower frequency band, the design of vibration and noise reduction schemes is more difficult, and it is necessary to combine sound radiation mechanisms to formulate a more effective noise reduction scheme. If only a single damping measure is used, aiming at reducing the vibration, it is difficult to reduce the BGB radiation acoustic waves. The mechanisms involved in the two types of BGB noise reduction via top plate thickening and the key issues show that, by changing the vibration distribution of the BGB, the peak sound radiation, as determined by the characteristics of the BGB itself, can be reduced, so damping the vibration and changing the vibration distribution can be combined to achieve a better noise reduction effect. The top plate of the BGB is the most important factor contributing to its acoustic radiation, and it should be considered in noise reduction design. Reducing the vibration characteristics of the top plate of the BGB (reducing the vibration amplitude and changing the vibration distribution) will directly determine the noise reduction effects of the design. Although the top plate thickening design scheme increases the vibration in the rest of the plate to a certain extent, it significantly affects the vibration suppression of the top plate of the BGB, so it can play a vital role in the noise reduction design. The following problems with the current design model of using thickened top plates for noise reduction are worthy of further research:  
* It is difficult in the current study to accurately determine the optimal thickness of the top plate of a low-noise-radiating BGB that meets all other requirements.