# Vibration Response Characteristics of Prefabricated Frame Structures Around the Subway
## 5 Vibration Response Characteristics of Prefabricated Frame Structures Around Subways
### Influence of Column Cross-Section Variation on the Structural Vibration Response  
Variations in column cross-section significantly impact overall structural stiffness, consequently inducing distinct vibration characteristics in subway environments. The baseline structure from Section 2 served as the analytical basis for column cross-section variations, with structural layout details shown in Figure 3. While preserving original component specifications, column sectional sizes were systematically altered, with parametric configurations tabulated in Table 8.  
Consistently with Section 2's design criteria, structural parameters were input into PKPM2025R2.3 to generate reinforcement layouts for all models. Uniform column reinforcement patterns based on ground-floor central column designs were implemented across models, with cross-sectional reinforcement details illustrated in Figure 12. Joints utilized four M20 (Grade 8.8) high-strength friction-grip bolts in a dual-row symmetric arrangement, with 12 mm splice plates matching parent material properties. Translational stiffness \(K_{\mathrm{v}}=2.8\times 10^{9}\) N/m and rotational stiffness \(K_{\mathrm{r}}=1.83\times 10^{8}\) N\(\cdot\)m/rad were assigned, with structural \(\gamma\) maintained at 0.5. Bushing connectors simulated semirigid joints for the Z1-S/Z2-S/Z3-S models, while Beam connectors represented ideal rigid joints in the Z1-R/Z2-R/Z3-R series. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & **Z1-S** & **Z1-R** & **Z2-S** & **Z2-R** & **Z3-S** & **Z3-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 & & & & & & \\ mm \(\times\) mm & 450 \(\times\) 450 & 450 \(\times\) 450 & 500 \(\times\) 500 & 500 \(\times\) 500 & 550 \(\times\) 550 & 550 \(\times\) 550 \\ Beam section & & & & & & \\ mm \(\times\) mm & 250 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 500 & 250 \(\times\) 500 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Design parameters of components of the variable column section model. Triaxial vibration signals (X/Y/Z directions) generated by an 80 km/h six-car metro train above the tunnel's central axis were applied to the six models through a base-uniform excitation protocol. After signal processing of midspan edge beam nodal vibrations, frequency-weighted acceleration levels across floor monitoring points were obtained as shown in Figure 13.  
Globally, frames with rigid connections demonstrated weighted acceleration magnitudes reduced by 2-4 dB per floor relative to semirigid systems under equivalent column sectional dimensions. Rigid connection models achieved up to 2 dB vibration reduction through column section enlargement, while semirigid systems attained approximately 1 dB attenuation via similar modifications. This disparity arose from rigid joints creating fully fixed connections that enhance structural integrity, enabling complete transfer of column bending stiffness to global system rigidity. The restricted rotational capacity of semirigid connections impedes full lateral stiffness realization, as column stiffness improvements are partially dissipated through joint flexibility rather than contributing to holistic structural enhancement. According to Standard [11] vibration thresholds, structures with 450 mm \(\times\) 450 mm or 500 mm \(\times\) 500 mm column sections employing semirigid joints exceeded residential night  
Figure 12: Detailed drawings of the variable column sections: (**a**) Z1-S, Z1-R; (**b**) Z2-S, Z2-R; (**c**) Z3-S, Z3-R.  
Figure 13: Frequency-weighted acceleration levels of the middle nodes of the side beams on each floor in different column section models. time acceleration limits.