# Seismic Response Effect on Base-Isolated Rigid Structures by Mass Eccentricity in Nuclear Plants
## 3 Sensitivity Analysis of Base Isolation Response Due to Mass Eccentricity
### Results of the Sensitivity Analysis of Seismic Response by Mass Eccentricity  
First, we aimed to examine the changes in the dynamic characteristics of the base-isolated structure as the eccentricity increased. Modal analysis results indicate that for 0% eccentricity (non-eccentric), the first, second, and fourth modes appear as translational (X, Y, Z) modes, the third mode as a horizontal torsional (rotation) mode, and the fifth and sixth modes as vertical rocking modes as shown in Table 3. As mass eccentricity increases, when observing changes in the dynamic characteristics of the base-isolated upper structure, torsional modes appear in lower-order modes, and, in some translational modes, a mixed mode with torsional behavior becomes more evident. Figure 3: Definition of mass eccentricity value in Y direction and locations of A1 to A4 points. Figure 2: Sensitivity analysis models for a base-isolated structure. (**a**) Dummy mass on the LRB model; (**b**) Dummy mass on the equivalent spring model. As the mass eccentricity increases, the contribution of the torsional mode increases, leading to a mixed behavior of translational and torsional modes in the structure [15]. To summarize, the changes in the natural frequencies of each mode as the horizontal single-axis mass eccentricity increases were observed and are presented in Figure 4. As the mass eccentricity of the base-isolated upper structure increases from 0% to 100%, the natural frequency of the first mode does not decrease much; however, the source of mode behavior changes from translation to a combination of translation and rotation. This is likely due to the torsional behavior caused by mass eccentricity. The second mode remains unaffected by horizontal direction eccentricity, as expected. In the case of the third mode, the frequency actually increases from 3.3 Hz to 4.6 Hz. This is attributed to an increase in the contribution of the first mode due to eccentricity, coupled with a decrease in horizontal torsion due to no eccentricity. The fifth mode, similar to the second mode, remains unaffected by eccentricity, resulting in no change in its natural frequency. The fourth and sixth modes exhibit characteristics similar to the changes observed in the first and third modes. Therefore, when the upper structure of the base-isolated structure experiences mass eccentricity, the torsional mode becomes the dominant mode, leading to changes in dynamic behavior with increased contributions to the response. Next, to examine structural response characteristics for the input of seismic motion, 3D seismic response analysis was conducted using the design response spectrum (DRS) applied in domestic export-standard nuclear power plants, as shown in Figure 5. In Figure 5a, the horizontal direction (EW) DRS is compared with the test response spectrum (TRS) and the required response spectrum (RRS). In Figure 5b, the acceleration time history corresponding to the DRS is shown. Figure 4: Change in modal frequencies with eccentricity. (**a**) Frequencies for Mode-1 to Mode-3; (**b**) Frequencies for Mode-4 to Mode-6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**0\% Eccentricity**} & \multicolumn{2}{c}{**100\% Eccentricity**} \\ \hline
**Mode** & **Hz** & **Mode Shapes** & **Hz** & **Mode Shapes** \\ \hline
1 & 2.3 & Translation (X) & 1.7 & Translation (X) + Rotation (RZ) \\
2 & 2.3 & Translation (Y) & 2.3 & Translation (Y) \\
3 & 3.3 & Rotation (RZ) & 4.6 & Rotation (RZ) \\
4 & 36.9 & Translation (Z) & 22.7 & Translation (Z) + Rocking (RX) \\
5 & 50.5 & Rocking (RY) & 50.5 & Rocking (RY) \\
6 & 53.2 & Rocking (RX) & 86.6 & Rocking (RX) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mode characteristics based on eccentricity in base-isolated structures. Next, to observe the seismic response impact of the eccentricity in a base-isolated structure, the average acceleration response at the center of the upper structure is analysed and reviewed. Within an eccentricity of 10%, both the X and Y directions show minimal changes in acceleration.