# 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
Increasing column dimensions effectively constrained weighted acceleration levels within nighttime residential limits, though significant gaps persisted relative to daytime thresholds. Sustained occupant comfort would require either joint stiffness augmentation or integrated vibration control strategies for residential applications. Comparative analysis with Figure 8 demonstrates that column section modifications induced greater weighted acceleration level variations than equivalent beam section adjustments. This effect was amplified in rigid-jointed systems, indicating columns' higher participation factors in vibration energy transmission--column parameter alterations provoked more substantial system response deviations. To further analyze the pattern of the structural vibration response changes under the subway environment caused by the variation of column cross-sections, the vertical acceleration time-history data at the middle nodes of the top-side beams of models with different column cross-sections were extracted and converted into spectral data. The results are shown in Figure 14.  
Spectral waveform characteristics remained relatively stable when varying column dimensions and joint configurations under equivalent excitation conditions. Column section modifications in semirigid systems shifted the dominant vibration energy to 10-15 Hz bandwidths, whereas rigid-jointed configurations preserved 30 Hz-centered spectral distributions despite parametric changes. This indicates that rigid joints minimized modal sensitivity to column changes, while semirigid configurations demonstrated heightened mode shape susceptibility to column variations, significantly affecting spectral peak characteristics. Semirigid-jointed structures exhibited pronounced upward shifts in dominant vibration frequencies with column section enlargement. This frequency escalation stemmed from enhanced global stiffness outweighing mass effects during column enlargement, as natural frequencies are proportional to stiffness and inversely related to mass. Rigid joints' inherent high stiffness established elevated baseline frequencies, making subsequent column changes induce negligible frequency variations. However, Figure 14b reveals amplitude attenuation at characteristic frequencies with column enlargement, indicating that increased column dimensions primarily affected vibration energy distribution across frequency bands in rigid systems. Figure 14: Acceleration spectra of the middle nodes of the side beams on the top floor in different column section models: (**a**) semirigid-jointed systems; (**b**) rigid-jointed systems. To further study the influence of the variation of column cross-sections on the structural vibration velocity in the time domain, the X- and Y-direction velocity time histories at the central position of the top floor of each structure were extracted, as shown in Figure 15. The peak velocities in the time domain were extracted and are shown in Table 9.  
Time-domain analyses revealed that even the maximum column section within the parametric range exceeded nonresidential/nonindustrial vibration velocity limits. While converting to rigid connections and enlarging column sections effectively reduced peak velocities, stricter compliance would demand additional mitigation measures--continuous column enlargement exhibited diminishing returns. Column enlargement demonstrated superior Y-direction peak velocity reduction efficacy (max 11.22%) compared with X-direction effects. As Table 7 indicates, column modifications outperformed beam section changes in peak velocity mitigation. This superiority persisted in semirigid systems, where column enlargement provided greater velocity reduction than beam modifications. Thus, column parameter optimization delivers superior cost-benefit ratios in vibration control design.