## 5 Key Issues of BGB Top Plate Thickening Design in Acoustic Vibration Control
### Exploration of the Key Influence of Vibration Distribution of BGB on Its Sound Radiation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Acoustic Vibration** & **Characteristic Index** & **Initial BGB** & **Whole Thickened** & **Local Thickened Top** \\
**Characteristics** & & & **Top Plate of BGB** & **Plate of BGB** \\ \hline \hline \multicolumn{5}{c}{Low Frequency Band} \\ \hline Self-oscillation—2 nd order & Inherent frequency (Hz) & 7.0 & 6.5 & 6.7 \\ mode & Description of vibration type & Bridge first-step vertical bend & Bridge first-step vertical bend & Bridge first-step vertical bend \\ Vibration characteristics & Vibration frequency (Hz) & 6.8 & 6.8 & 6.8 \\ by external excitation & Vibration pattern (maximum & First step overall vertical bend & First step overall & First step overall \\  & amplitude—m/s\({}^{2}\)) & (0.20) & vertical bend (0.10) & vertical bend (0.12) \\ Acoustic radiation & Acoustic radiation efficiency & 0.11 & 0.09 & 0.09 \\ characteristics & Sound Power & 115.7 & 106.5 & 107.8 \\ \hline \multicolumn{5}{c}{Resonance phenomenon formed by BGB} \\ \hline Self-oscillation—10 th & Inherent frequency (Hz) & 21.0 & 24.3 & 23.8 \\ order mode & Description of vibration type & Overall bridge vibration & Bottom plate local & Bottom plate local \\ Vibration characteristics & Vibration frequency (Hz) & 21.4 & 24.8 & 23.7 \\ by external excitation & Vibration pattern (maximum & Bridge overall bending & Top plate local & Local vibration at both ends of the top plate \\  & amplitude—m/s\({}^{2}\)) & vibration (0.60) & vibration (0.54) & (0.24) \\ Acoustic radiation & Acoustic radiation efficiency & 3.74 & 0.66 & 0.40 \\ characteristics & Sound Power & 120.2 & 110.6 & 98.7 \\ \hline \multicolumn{5}{c}{Acoustic radiation efficiency of BGBs} \\ \hline Self-oscillation—12 th & Inherent frequency (Hz) & 23.7 & 2.0 & 27.8 \\ order mode & Description of vibration type & Top plate local vibration & All plates local & All plates local \\ Vibration characteristics & Vibration frequency (Hz) & 23.7 & 29.3 & 27.1 \\ by external excitation & Vibration pattern (maximum & Local vibration at both ends of & Top plate local & Top/web plate Local \\  & amplitude—m/s\({}^{2}\)) & the top plate (0.37) & vibration (0.16) & vibration (0.17) \\ Acoustic radiation & Acoustic radiation efficiency & 2.54 & 0.60 & 0.78 \\ characteristics & Sound Power & 117.8 & 98.6 & 103.3 \\ \hline \multicolumn{5}{c}{Acoustic radiation efficiency of BGBs} \\ \hline Self-oscillation—18 th & Inherent frequency (Hz) & 36.7 & 46.6 & 42.1 \\ order mode & Description of vibration type & Top plate local vibration & Bottom plate local & Wing plate local \\ Vibration characteristics & Vibration frequency (Hz) & 37.2 & 46.2 & 41.7 \\ by external excitation & Vibration pattern (maximum & All plates local & Top plate local \\  & amplitude—m/s\({}^{2}\)) & Top plate local vibration (0.09) & All plates local & Top plate local \\  & amplitude—m/s\({}^{2}\)) & \multicolumn{2}{c}{} & vibration (0.31) & vibration (0.72) \\ Acoustic radiation & Acoustic radiation efficiency & 0.89 & 0.71 & 0.58 \\ characteristics & Sound Power & 104.1 & 102.7 & 107.3 \\ \hline \multicolumn{5}{c}{Resonance phenomenon formed by BGB} \\ \hline Vibration characteristics & Vibration frequency (Hz) & 93.6 & 93.6 & 93.6 \\ by external excitation & Vibration pattern (maximum & All plates local & All plates local & All plates local \\  & amplitude—m/s\({}^{2}\)) & \multicolumn{2}{c}{} & vibration (1.20) & vibration (1.07) \\ Acoustic radiation characteristics & Acoustic radiation efficiency & 108.5 & 106.2 & 105.0 \\ \hline \multicolumn{5}{c}{Key influencing factors of acoustic radiation} \\ \hline Key influencing factors of acoustic radiation & & Severe vibration formed by BGBs (vibration reduction) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of acoustic vibration characteristics of BGBs used in a high-speed railway under three working conditions. From the sound vibration characteristics of the BGB shown in Table 3, it can be seen that: (1) The BGBs under the three conditions have similar inherent frequencies at 6.8 Hz.