# 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  
The baseline structure from Section 2 served as the basis for variable beam cross-section analysis, maintaining constant parameters for other components while varying beam dimensions to achieve different height-width ratios. Component parameters for different models are specified in Table 5.  
With identical design specifications as the Section 2 baseline model, reinforcement detailing was generated through the PKPM2025R2.3 software, with beam reinforcement configurations illustrated in Figure 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Area** & **Strict Area** & **Residential Area** & **Office Area** & **Production Line** \\ \hline Daytime & 74 & 80 & 86 & 92 \\ Nighttime & 74 & 77 & 86 & 92 \\ \hline \hline \end{tabular} Note: The strict vibration zone refers to work areas with strict vibration requirements, such as operating rooms in hospitals.  
\end{table} 
Table 4: Allowable vibration weighted acceleration levels for human comfort in buildings under repetitive vibration action (dB) [11]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & **L1-S** & **L1-R** & **L2-S** & **L2-R** & **L3-S** & **L3-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 & 4 \\ Slab thickness mm & 100 & 100 & 100 & 100 & 100 & 100 \\ Column section & 500 \(\times\) 500 & 500 \(\times\) 500 & 500 \(\times\) 500 & 500 \(\times\) 500 & 500 \(\times\) 500 \\ mm \(\times\) mm & 250 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 550 & 250 \(\times\) 550 & 200 \(\times\) 500 \\ Aspect ratio & 2 & 2 & 2.2 & 2.2 & 2.5 & 2.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Design parameters of the variable-beam-section model components. Joints retained four M20 (Grade 8.8) high-strength friction-grip bolts in a double-row symmetric configuration, with 12 mm splice plates matching base material properties. Translational joint stiffness was maintained at \(K_{v}\) = 2.8 \(\times\) 10\({}^{9}\) N/m. With \(\gamma\) = 0.5, rotational stiffness values for various beam sections are presented in Table 6. Semirigid joint behavior in L1-S/L2-S/L3-S was modeled using Bushing connectors, whereas ideal rigid connections for L1-R/L2-R/L3-R were achieved through ABAQUS' Beam connector element in the Interaction module. Vibration time-history signals along the X/Y/Z directions generated by an 80 km/h operating six-car Type B train above tunnel central axis were implemented in the six models using the base-uniform excitation method. Vibration time-history data at midspan nodes of edge beams across all floors were extracted. After FFT processing, weighted acceleration levels at monitoring points were calculated using Equation (3) and ISO 2631-1 ([[https://www.iso.org/standards-catalogue/browse-by-ics.html](https://www.iso.org/standards-catalogue/browse-by-ics.html)]([https://www.iso.org/standards-catalogue/browse-by-ics.html](https://www.iso.org/standards-catalogue/browse-by-ics.html))) weighting factors, with results presented in Figure 8.  
Overall, structures with semirigid joints exhibited 3-4 dB higher weighted acceleration levels than rigidly connected structures. Regardless of joint rigidity configurations, structural vibration responses under subway environments showed consistent distribution patterns across floors, with slight amplification from base to top levels. The top floor exhibited 0.5-1 dB higher weighted acceleration levels than the first floor, analogous to vibration behavior in fixed-base cantilever column models. Vibration energy transmission from base excitation to free ends induces cumulative energy dissipation through structural oscillations, manifesting as amplified vibration magnitudes. The limited story count in the model attenuated significant amplification at upper levels.