# Vibration Response Characteristics of Prefabricated Frame Structures Around the Subway
## 5 Vibration Response Characteristics of Prefabricated Frame Structures Around Subways
### Influence of Beam Cross-Section Variation on the Structural Vibration Response
According to Code [11] regarding permissible weighted acceleration levels for human comfort under repetitive vibrations, structures with semirigid joints exceeded residential nighttime limits across all floors. Semirigid structures with 250 \(\times\) 500 mm beam sections exceeded daytime residential limits at certain floors, rendering this structural form unsuitable for residential use without effective vibration mitigation. While rigid-jointed structures complied with residential day/night limits, they exceeded stringent vibration zone require \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **L1-S** & **L2-S** & **L3-S** \\ \hline \(K_{r}\) N\(\cdot\)m/rad & 1.83 \(\times\) 10\({}^{8}\) & 2.41 \(\times\) 10\({}^{8}\) & 1.51 \(\times\) 10\({}^{8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values of nodal rotational stiffness for different beam section models. Figure 7: Detailed drawings of the variable beam sections: (**a**) L1-S, L1-R; (**b**) L2-S, L2-R; (**c**) L3-S, L3-R.  
ments. This demonstrates that beam section modifications inadequately control vibration levels within stringent zone limits, requiring supplementary mitigation strategies. From a beam-cross-sectional perspective, increasing beam height or enhancing the height-to-width ratio (while maintaining height) marginally reduces structural weighted acceleration levels, regardless of joint rigidity configurations. Height augmentation substantially increases the sectional moment of inertia, thereby enhancing beam flexural rigidity. This global stiffness improvement benefits vibration acceleration level control. Maintaining beam height while increasing aspect ratio (equivalent to width reduction) yields lower acceleration levels, attributed to modified stiffness relationships. Narrower beams marginally decrease flexural stiffness, reducing beam-column stiffness ratios, and studies have confirmed that higher stiffness ratios amplify structural displacement responses [12], so diminished stiffness ratios suppress overall structural vibration responses. For the parametric range investigated, aspect ratio adjustment achieved superior vibration control to that of height increase, with more significant effects observed in rigid connection systems. In semirigid configurations, vibration attenuation differences between height and aspect ratio modifications remained statistically insignificant. To further identify vibration response patterns of different beam sections under subway environments, vertical acceleration spectral data at midedge beam nodes of top floors were analyzed, as shown in Figure 9.  
All structural configurations exhibited similar spectral characteristics under identical base excitations, regardless of semirigid joint implementation or beam cross-sectional variations. However, rigid-jointed structures demonstrated dominant frequencies between 20 and 35 Hz, whereas semirigid configurations exhibited primary frequency concentrations within 10-15 Hz. This frequency disparity originated from joint stiffness effects on global stiffness matrices--increased nodal rigidity elevates structural stiffness and consequently enhances natural frequencies. Broadband subway vibrations potentially excite higher-order modes, explaining the elevated frequency ranges in rigid-jointed structures. Structural acceleration amplitude responses varied across beam cross-sections, generally exhibiting elevated dominant frequency bands with increasing aspect ratio. Previous analyses have revealed that beam aspect ratio modifications alter beam-column stiffness ratios, consequently affecting structural vibration characteristics. Beyond influencing  
Figure 8: Weighted acceleration levels of the middle nodes of the side beams on each floor in different beam section models. **Note:** The gray dashed lines represent the allowable vertical vibration values for residential areas at night and during the day, respectively.