# Vibration Response Characteristics of Prefabricated Frame Structures Around the Subway
## 5 Vibration Response Characteristics of Prefabricated Frame Structures Around Subways
### Influence of Slab Thickness Variation on the Structural Vibration Response
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & **B1-S** & **B1-R** & **B2-S** & **B2-R** & **B3-S** & **B3-R** \\ \hline \(\gamma\) & 0.5 & Rigid & 0.5 & Rigid & 0.5 & Rigid \\ Number of stories & 5 & 5 & 5 & 5 & 5 & 5 \\ Number of spans & 4 & 4 & 4 & 4 & 4 \\ Slab thickness mm & 100 & 100 & 110 & 110 & 120 & 120 \\ Column section & 500 \(\times\) 500 & 500 \(\times\) 500 & 500 \(\times\) 500 & 500 \(\times\) 500 & 500 \(\times\) 500 \\ Beam section & 500 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 500 \\ mm \(\times\) mm & 500 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 500 \\ \hline \end{tabular}
\end{table} 
Table 10: Design parameters of components in the variable-slab-thickness models. Figure 17: Weighted acceleration levels of the middle nodes of the side beams on each floor in different slab thickness models. strated greater vibration reduction per thickness increment but reached critical thickness earlier than their rigid counterparts. To further analyze the pattern of structural vibration response changes under subway environment caused by slab thickness variation, vertical acceleration time-history data at middle nodes of top-side beams in different models were extracted and converted into spectral data, as shown in Figure 18.  
Structures with varying slab thicknesses and joint connection types exhibited similar vibration spectral waveforms under identical excitation inputs, demonstrating low-frequency multimodal characteristics in the frequency domain. Rigid-jointed structures generally exhibited higher dominant frequencies than their semirigid counterparts. Increasing slab thickness did not significantly alter these dominant frequencies. For semirigid systems, increasing slab thickness from 100 mm to 110 mm raised the dominant frequency by 4 Hz, caused slight bandwidth expansion, and reduced peak amplitude by 10.01%. From 110 mm to 120 mm, dominant frequency remained stable while peak amplitude decreased by 8.66%. Approaching the critical thickness, frequency sensitivity diminished, with primary effects shifting to peak amplitude reduction. In rigid-jointed structures, each 10 mm slab increase elevated the dominant frequency by 2 Hz and reduced peak response by 10%, indicating stable vibration modulation within 100-120 mm range and sub-critical-thickness conditions. To further study the influence of slab thickness variation on structural vibration velocity in the time domain, the X- and Y-direction velocity time histories at the central position of the top floor in each structure were extracted, as shown in Figure 19. The peak velocities in the time domain are listed in Table 11.  
Overall, slab thickness variations demonstrated limited influence on horizontal velocity peaks. Y-direction peak velocities at monitoring points exceeded nonresidential/nonindustrial building thresholds despite slab thickening. In rigid-jointed structures, each 10 mm slab thickening achieved 4.5% Y-direction peak velocity reduction, while \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & **B1-S** & **B2-S** & **B3-S** & **B1-R** & **B2-R** & **B3-R** \\ \hline X mm/s & 1.635 & 1.541 & 1.497 & 1.484 & 1.417 & 1.379 \\ Y mm/s & 3.592 & 3.451 & 3.407 & 2.976 & 2.842 & 2.729 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Peak values of horizontal biaxial velocity at the central position of the top-floor slab in different models. Figure 18: Acceleration spectrum of the middle nodes of the top-floor side beams in different slab thickness models: (**a**) semirigid-jointed systems; (**b**) rigid-jointed systems. X-direction responses showed negligible changes. Y-direction peak velocity reduced during 110 to 120 mm thickening in semirigid configurations, revealing critical-thickness-induced performance degradation in velocity modulation.