## 6 Parameter Analysis  
### The Effect of Baffle  
Consider nondimensional baffle heights, the fluid height and the baffle inner radius as \(\beta_{i}=h_{i}/h_{M+1}\) (\(i=1,\ 2,\cdots,\ M\)), \(\beta_{M+1}=h_{M+1}/R_{2}\) and \(\gamma=R_{1}/R_{2}\), respectively. The near-fault (NF) and far-fault (FF) seismic records are given in detail in Table 3. Figure 7 depicts the variations of the first-order convective frequency \(\omega_{11}^{C}\) with regard to different baffle heights for \(M=2\), \(\beta_{3}=1.0\) and \(R_{2}=10\) m. The soil shear wave velocity vs. is fixed at 150 m/s. The height of the lower baffle exerts little impact on the first order convective frequency in Figure 7a, however, the first order convective frequency declines by increasing the upper baffle location in Figure 7b. Figure 8 illustrates the variation of the rotational impulsive frequency \(\omega_{1}^{\text{r}}\) for the baffle height. It is seen that the rotational impulsive frequency increases by increasing the height of the lower and/or upper baffle. In Figure 9, the impacts of the baffle inner radius on the frequency are presented. It is observed that the first-order convective sloshing frequency and horizontal impulsive frequency both increase by increasing the baffle inner radius. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(V_{\text{s}}\) (m/s)} & \multicolumn{3}{c}{\(\alpha_{1}\)} & \multicolumn{3}{c}{\(\alpha_{2}\)} & \multicolumn{3}{c}{\(\alpha_{3}\)} \\ \cline{2-10}  & **Present** & **Literature [30]** & **Errors** & **Present** & **Literature [30]** & **Errors** & **Present** & **Literature [30]** & **Errors** \\ \hline
150 & 1.9442 & 1.8412 & 5.59\% & 2.0398 & 1.9148 & 6.53\% & 1.1008 & 1.0525 & 4.59\% \\
200 & 1.8109 & 1.6652 & 8.75\% & 1.8394 & 1.7410 & 5.65\% & 1.2835 & 1.2030 & 6.69\% \\
250 & 1.5388 & 1.4484 & 6.24\% & 1.5690 & 1.5172 & 3.41\% & 1.2270 & 1.1619 & 5.60\% \\
600 & 1.2051 & 1.3190 & \(-8.63\%\) & 1.2416 & 1.3602 & \(-8.72\%\) & 0.9780 & 1.0012 & \(-2.32\%\) \\
800 & 1.0508 & 1.1324 & \(-7.21\%\) & 1.0933 & 1.1587 & \(-5.64\%\) & 1.2022 & 1.0024 & 1.78\% \\
1200 & 1.0204 & 1.0430 & \(-2.17\%\) & 1.0210 & 1.0882 & \(-6.18\%\) & 1.0085 & 1.0012 & 0.73\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of responses between present results and those obtained from an analytical model [30]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Earthquake** & **RSN** & **Event** & **Year** & **Station** & \(\mathbf{T_{p}}\) **(s)** & **Record** & **PGA (g)** \\ \hline NF & 1106 & Kobe & 1995 & KJMA & 1.092 & KJM-000 & 0.834 \\ FF & 154 & Coyote Lake & 1979 & San Juan & - & SJB-303 & 0.106 \\  & & & & Bautista & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Details of near-fault and far-fault earthquake records. Figure 8: The rotational impulsive frequency for the baffle height: (**a**) the height of the lower baffle \(\beta_{1}\); (**b**) the height of the upper baffle \(\beta_{2}\). Figure 7: The first-order convective frequency for the baffle height: (**a**) the height of the lower baffle \(\beta_{1}\); (**b**) the height of the upper baffle \(\beta_{2}\). Figure 9: Influence of the baffle inner radius \(\gamma\) on the frequencies: (**a**) the first-order convective frequency; (**b**) the horizontal impulsive frequency. The amplitudes of the surface height at the wall \(f_{\text{wall}}\) associated with the location and size of the upper baffle are presented in Figure 10 for \(M=2\) and \(R_{2}=0.508\) m. The motion amplitude for the tank is \(X_{0}=0.001\) m and horizontal harmonic excitation frequency is \(\varpi=5.811\) rad/s. The liquid height is 0.508 m. It is seen that as the baffle height increases, \(f_{\text{wall}}\) monotonically declines, however, \(f_{\text{wall}}\) monotonically increases as the inner radius increases. Result indicates that the existence of the annular baffles can significantly mitigate the surface height.