# Vibration Response Characteristics of Prefabricated Frame Structures Around the Subway
## 5 Vibration Response Characteristics of Prefabricated Frame Structures Around Subways
### Influence of the Total Structural Stories Variation on the Structural Vibration Response
To further investigate the influence of variations in the total number of stories on the time-domain vibration velocity of the structure, the X-/Y-direction velocity time histories at the center of the top floor of each structure were extracted and are shown in Figure 24, while the peak time-domain velocities are listed in Table 13.  
Progressive heightening induced systematic Y-direction velocity attenuation (5% to 7% per three stories) at the roof center, demonstrating logarithmic decay characteristics in horizontal vibration components. This phenomenon originates from subway vibration transmission through vertical members: dominant axial waves experience progressive \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Direction**} & \multicolumn{2}{c}{**Five-Story Model**} & \multicolumn{2}{c}{**Eight-Story Model**} & \multicolumn{2}{c}{**Eleven-Story Model**} \\ \cline{2-7}  & **X** & **Y** & **X** & **Y** & **X** & **Y** \\ \hline Peak & 1.653 & 3.592 & 1.371 & 3.334 & 1.175 & 3.176 \\ velocity & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Peak values of horizontal biaxial velocity at the central position of the top-floor slab in different models mm/s. Figure 24: Horizontal biaxial velocity time-history diagrams at the central positions of the top-floor slabs of different models: (**a**) the 5-story model; (**b**) the 8-story model; (**c**) the 11-story model. attenuation with height, while reflected waves at the roof level induce secondary horizontal vibrations. The cumulative axial wave attenuation ultimately governs peak velocity reduction at upper floors. While Y-direction peaks complied with residential limits, all configurations exceeded stringent zone thresholds. Continued heightening proved ineffective for strict compliance, necessitating supplemental vibration control measures for critical applications. To assess the frequency-dependent energy accumulation caused by metro vibrations in structures with different total story numbers, mixed-direction acceleration time histories were collected from midspan nodes of edge beams at the first-, intermediate-, and top-floor levels. The data were processed via FFT to derive the corresponding spectral data, as illustrated in Figure 25.  
Across structural configurations with varying total stories, mixed-direction velocity responses were predominantly concentrated within the 10-15 Hz frequency range. While the dominant frequency exhibited slight upward shifts with increasing story counts, the spectral energy distribution remained anchored in low-frequency domains. The frequency bandwidth of mixed-direction velocity responses progressively narrowed with structural heightening, resulting from heightened modal frequency concentration and simplified vibration patterns, ultimately manifesting as multipeak narrowband spectral characteristics. Spectral characteristics diverged across vertical monitoring positions: ascending floors exhibited (1) downward frequency migration, (2) high-frequency component attenuation,  
Figure 25: Mixed-direction velocity frequency spectrum diagrams at the measuring points on each floor of models with different numbers of stories: (**a**) the 5-story model; (**b**) the 8-story model; (**c**) the 11-story model. and (3) multipeak emergence in the sub-5 Hz range. This spectral evolution originated from wave reflection dynamics at the structural apex, where superposition of incident and reflected waves generates multiple resonance peaks.