# Base Pounding Model and Response Analysis of Base-Isolated Structures under Earthquake Excitation
## 3 Engineering Case and Numerical Simulation
### Effects of Pounding
#### 3.2.3 Acceleration  
Figures 16 and 17 show the acceleration time-history curves of node 858, where the maximum values of acceleration were observed, under different earthquake excitations. The maximum accelerations that were obtained in models A and B are presented in Tables 4 and 5.  
When compared to cases without bounding, a large amplification can be observed in both models A and B under bounding condition, according to Figures 16 and 17. Furthermore, the maximum values of acceleration appear when excitations are strong.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Earthquake** & **Range of Maximum Value** & \begin{tabular}{c} **Without Pounding** \\ **(kN)** \\ \end{tabular} & \begin{tabular}{c} **With Pounding** \\ **(kN)** \\ \end{tabular} & \begin{tabular}{c} **With Pounding** \\ **(kN)** \\ \end{tabular} & \begin{tabular}{c} **Times of Growth** \\ \end{tabular} \\ \hline El Centro & \begin{tabular}{c} low limit \\ upper limit \\ \end{tabular} & 466 & 2828 & 5.06 \\ \hline \multirow{2}{*}{Taft} & \begin{tabular}{c} low limit \\ upper limit \\ \end{tabular} & 539 & 2223 & 3.13 \\  & \begin{tabular}{c} upper limit \\ \end{tabular} & 8715 & 26,546 & 2.04 \\ \hline \multirow{2}{*}{Artificial} & \
\begin{tabular}{c} low limit \\ upper limit \\ \end{tabular} & 450 & 1636 & 2.63 \\  &
\begin{tabular}{c} 8450 \\ \end{tabular} & 17,213 & 1.03 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Maximum values of story shear-force for model A.  
Figure 16: Structural acceleration under different earthquakes (model A). (**a**) El Centro earthquake; (**b**) Taft earthquake; and, (**c**) Artificial excitation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Earthquake** & **Range of Maximum Value** & \begin{tabular}{c} **Without Pounding** \\ **(kN)** \\ \end{tabular} & \begin{tabular}{c} **With Pounding** \\ **(kN)** \\ \end{tabular} & \begin{tabular}{c} **With Pounding** \\ **(kN)** \\ \end{tabular} & \begin{tabular}{c} **Times of Growth** \\ \end{tabular} \\ \hline El Centro & \begin{tabular}{c} low limit \\ upper limit \\ \end{tabular} & 238 & 3238 & 12.60 \\  & \begin{tabular}{c} upper limit \\ \end{tabular} & 12,350 & 32,000 & 1.59 \\ \hline \multirow{2}{*}{Taft} & \begin{tabular}{c} low limit \\ upper limit \\ \end{tabular} & 240 & 2864 & 10.93 \\  & \begin{tabular}{c} upper limit \\ \end{tabular} & 13,080 & 29,950 & 1.30 \\ \hline \multirow{2}{*}{Artificial} & \
\begin{tabular}{c} low limit \\ upper limit \\ \end{tabular} & 386 & 1636 & 3.24 \\  &
\begin{tabular}{c} upper limit \\ \end{tabular} & 21,114 & 17,213 & \(-0.18\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Maximum values of story shear-force for model B.  
According to Tables 4 and 5, for model A under bounding conditions, there is a 4.88 times growth in acceleration under the El Centro earthquake, a 3.42 times growth under the Taft earthquake, and a 2.82 times growth under the Artificial earthquake. The amplification of model A is larger than that of model B, which was 12.67 times growth under the El Centro earthquake, 10.77 times growth under the Taft earthquake and 6.52 times growth under the Artificial earthquake.  
There are great bounding effects on acceleration on top story acceleration of both the structure with lead-rubber bearing and the structure with friction pendulum isolation bearing. However, the acceleration amplification of the structure with friction pendulum isolation bearing is larger.