# 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
global stiffness matrices, aspect ratio variations (under constant cross-sectional area conditions) modify beam mass distributions, consequently altering system mass matrices. As mass matrix constitutes a critical vibration determinant, the observed frequency escalation under aspect ratio enhancement aligns with theoretical expectations for the parametric variations investigated. The aspect-ratio-induced frequency amplification effect was more pronounced in rigid-jointed structures. For semirigid systems, reduced rotational stiffness weakens low-frequency vibration attenuation because of semirigid joints' influence on the first two natural frequencies, resulting in complex aspect-ratio-dependent frequency modulation patterns. In addition to evaluating human comfort through structural acceleration responses, investigating vibration kinetic energy transmission via velocity parameters [13] is crucial for understanding transient structural impacts induced by peak velocities in the time domain. X-/Y-direction velocity time-history diagrams at central roof locations are shown in Figure 10, with corresponding time-domain peak velocities extracted in Table 7.  
The two-axis horizontal peak velocities at roof centers of all models remained below residential building thresholds, indicating that the beam sections met structural safety requirements for residential applications. However, horizontal peak velocities exceeded permissible levels for nonresidential and nonindustrial structures. Rigid-jointed systems exhibit 8.47% lower peak velocities than semirigid counterparts, suggesting reduced long-term subway vibration impacts on rigid-connected structures. Beam section enlargement significantly reduces Y-axis peak velocities while marginally decreasing X-axis responses. Height-constant aspect ratio enhancement moderately decreases biaxial velocities, though less effectively than direct height increases, therefore, beam height enhancement proves optimal for mitigating subway vibration effects on structural health and ensuring long-term safety. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **L1-S** & **L2-S** & **L3-S** & **L1-R** & **L2-R** & **L3-R** \\ \hline X mm/s & 1.635 & 1.574 & 1.598 & 1.484 & 1.347 & 1.375 \\ Y mm/s & 3.592 & 3.314 & 3.437 & 2.976 & 2.724 & 2.793 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Peak values of horizontal biaxial velocity at the center of the top-floor slab in different models. Figure 9: Acceleration spectrum of the middle nodes of the side beams on the top floor in different beam section models: (**a**) semirigid-jointed systems; (**b**) rigid-jointed systems. Beyond time-domain analysis of subway vibration impacts, frequency-domain velocity investigations are required to identify critical frequency bands prone to energy accumulation and structural fatigue damage. Combined directional velocity time-history data at middedge beam nodes of top floors were extracted and processed via FFT, yielding composite velocity spectral data shown in Figure 11.  
Structural velocity spectra were predominantly concentrated in low-frequency ranges across all configurations. Under identical excitation inputs, composite velocity spectral pat  
Figure 11: Mixed-direction velocity spectrum of the middle nodes of the side beams on the top floor in different beam section models: (**a**) semirigid-jointed systems; (**b**) rigid-jointed systems. Figure 10: Time-history diagrams of horizontal biaxial velocity at the center of the top-floor slab in different models: (**a**) L1-S; (**b**) L2-S; (**c**) L3-S; (**d**) L1-R; (**e**) L2-R; (**f**) L3-R.  
terns exhibited similar low-frequency multipeak characteristics regardless of joint types or beam cross-sections. This phenomenon originated from subway vibration energy concentration in low frequencies, where structural fundamental frequencies intersecting with dominant subway spectral components induce resonant peaks.