# Shaking Table Tests of Suspended Structures Equipped with Viscous Dampers
## 4 Experimental Results and Discussion
### Acceleration Response  
Since the same peak acceleration of the vibration table input will give different responses under dissimilar working conditions, the acceleration amplification factor is used to characterize the power amplification effect. The acceleration amplification factor K\({}_{\text{F}}\) is the ratio of the peak acceleration of \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mode Shape**} & \multicolumn{2}{c}{**Conventional Suspended Structure**} & \multicolumn{2}{c}{**Damping Suspended Structure**} \\ \cline{2-5}  & **Frequency (Hz)** & **Damping Ratio (\%)** & **Frequency (Hz)** & **Damping Ratio (\%)** \\ \hline
1 & 5.21 & 2.301 & 1.50 & 9.254 \\
2 & 10.74 & 0.813 & 3.71 & 5.879 \\
3 & 12.24 & 0.710 & 6.24 & 3.362 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Frequency and damping ratio of model. each floor to the peak acceleration of the shaking table in the corresponding direction, which can be defined as:  
\[K_{iF}=\frac{\text{max}(a_{i}(t))}{\text{max}\Big{(}a_{g}(t)\Big{)}} \tag{1}\]  
where \(a_{i}(t)a_{i}(t)\) and \(a_{g}(t)a_{g}(t)\) are the acceleration response measured by the accelerometers arranged at the \(i\)th floor and the shaking table, respectively. The operation'max' is applied to all the data of the acceleration time history. [PERSON] et al. [27] and [PERSON] et al. [28] used this formula to calculate the amplification factors of structures. The variations of acceleration amplification factor K\({}_{\text{F}}\) of two structural models under various level seismic inputs are shown in Figure 8.  
As displayed in Figure 8, the acceleration response of K\({}_{\text{F}}\) displayed a consistent change and significantly increased with the height. The acceleration amplification factors of each structural model at the first two floors did not change much, primarily owing to the lateral stiffness of the bottom, which was relatively large. From the observation on the degree of changes in value, it is clear that the acceleration amplification factors on the fourth floor and above grew rapidly, and the difference between the three seismic waves was large. The top acceleration amplification factor of the two test models did not change much with the increase of seismic intensity, and the value was in the range of 1.6 to 2.0. This indicates that the structure models kept in elastic condition during the test process. Additionally, the acceleration amplification factors of the primary structure's top under dissimilar seismic waves were moderately different. Figure 8: Amplification factor of acceleration. (**a**) 7 frequent earthquake; (**b**) 8 frequent earthquake; (**c**) 9 frequent earthquake; (**d**) 7 rare earthquake; (**e**) 8 rare earthquake. It is noted that the acceleration amplification factors of the damping suspended structure were moderately smaller than those of the conventional suspended structure, and, under the different seismic levels, the difference between the amplification factors of the two structures under the Taft wave was the largest, which means that the suspended structure under the Taft wave had the best damping effect. The finding indicated that the acceleration amplification factor of the structure was not only affected by the input seismic intensity, but also depended on the frequency spectrum characteristics of the seismic wave. Figure 9 presents the acceleration time history curve of the primary structure's top of two types of suspended structure under the 9 frequent earthquake. As can be seen from Figure 9, the peak acceleration response of the damping suspended structure was less than and slightly behind the conventional suspended structure. Under the Taft wave, the peak acceleration response of the damping suspended structure reduced significantly, and the reduction  
Figure 9: Acceleration time history curves at top of primary structure under 9 frequent earthquake. (**a**) Acceleration time history under El Centro; (**b**) Acceleration time history under Taft; (**c**) Acceleration time history under artificial wave.