# 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
Figure 22: Weighted acceleration levels of the middle nodes of the side beams on each floor of models with different total numbers of stories. enhanced structural mass at higher story counts--with fixed foundation column quantities, similar vibration energy inputs distribute across larger masses, resulting in lower global acceleration magnitudes under equivalent excitations. Under identical subway operational and site conditions, five-story structures exceeded daytime residential limits at certain floors. At eight stories, levels complied with daytime thresholds but violated nighttime limits. When extended to 11 stories, all floors satisfied nighttime criteria. Thus, structural story count must be integrated into comfort evaluations for subway-adjacent buildings. Low-rise structures (\(n<11\)) showed monotonically increasing vibration levels with height. Beyond the critical height (\(n=11\) in this study), levels first decreased and then increased because of axial wave propagation in vertical members. Vibration energy reflects at the roof level without transmission medium, causing wave superposition and top-floor amplification [15]. As the story count increased, enlarged lower-floor member cross-sections enhanced stiffness and mass. This dual effect transformed vibration distribution patterns from monotonic growth to initial attenuation followed by amplification when reaching critical heights. Semirigid joints induced stronger reflection of axial and bending waves at connections than rigid joints, resulting in more pronounced floor-level vibration amplification effects in semirigid framed structures. To investigate vibration response patterns under varying story counts in subway environments, vertical acceleration time histories at middge beam nodes of top floors were analyzed through FFT processing and one-third octave band level calculations, with results presented in Figure 23.  
Figure 23: One-third octave vibration levels 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. In general, the peak distributions of the one-third octave band curves for each structural layer were quite close. The dominant frequency of the 5-story structure was approximately 16-20 Hz, that of the 8-story structure was around 12.5-20 Hz, and that of the 11-story structure was approximately 25-31.5 Hz. This was attributed to the increased stiffness of lower structural components required as the total number of stories increased, which altered the structure's sensitive frequency range. The energy of ground vibrations caused by metro operation is concentrated in the 30-60 Hz range, which is prone to resonating with the structural modes within this frequency band. Regardless of the total number of stories, the low-frequency components (below 10 Hz) experienced only slight attenuation as vibration waves propagated through the structure. In contrast, the high-frequency components (above 40 Hz) showed more significant attenuation during propagation, with a high-frequency amplitude reduction of over 10 dB between the top and the first floor. The five-/eight-story models shared similar spectral characteristics: high-frequency components attenuated rapidly while low frequencies persisted, indicating wave-reflection-induced energy accumulation at upper floors. The 11-story structure exhibited middle-floor (4-7F) vibration attenuation within the 16-20 Hz range, contrasting with lower-/higher-floor amplification. This \"saddle-shaped\" distribution arises from wave reflection dynamics: roof-reflected waves (affecting up to 7F) destructively interfere with incident waves at specific middle floors.