# Seismic Response Effect on Base-Isolated Rigid Structures by Mass Eccentricity in Nuclear Plants
## 5 Shaking Table Test for Base-Isolated Structures with Mass Eccentricity  
To assess the seismic response impact caused by the mass eccentricity of the base-isolated upper structure, sensitivity analysis and simulation analysis were conducted, as explained earlier. Subsequently, to validate the analysis results obtained, actual tests were carried out using a three-axis vibration table. It is worth noting that the vibration table used in this test had a capacity of 30 tons for dynamic experiments in three directions, and its detailed specifications can be found in Table 7. The test models consisted of the upper structure supported by four small LRBs, as previously described. Specifically, three models were used, each with different mass eccentricities, as shown in Figure 13. Additionally, to investigate the impact on the secondary structure, three different substructures, designed to have natural frequencies of 5 Hz, 10 Hz, and 30 Hz, were attached to the test table and upper structure, respectively, for response measurements [16]. Figure 13: Testing of mass eccentric structures using a 3-D table. (**a**) Schematic of sensor locations on the Eccl structure; (**b**) Preparation configuration for the 3-D table test. Figure 13a shows the sensor locations and beam models for the test of the eccentric mass 1 (Ecc1) structure as an example, and Figure 13b shows the picture of the actual test setup. Two sets of three different beams were installed both on the shaking table and also on the top of the eccentric mass structures to investigate the mass eccentricity effect of the upper structure on the seismic response of the secondary structure. This setup was designed to assess the response impact on the secondary structure in both the X and Y directions. When actual vibration tests were conducted using the seismic input data from Figure 5, it was observed that the acceleration response of the base-isolated superstructure decreased in the frequency range of interest around 5 Hz to 50 Hz, as shown in Figure 14 [16]. Specifically, a peak occurred around the frequency of the small base isolator's isolation frequency, approximately near 2.3 Hz, as expected. The response gradually decreased up to around 20 Hz and then maintained a relatively constant value for the remaining frequency range. As shown in Figure 15, it can be observed that, for the Ecc1 and Ecc2 models (e.g., with mass eccentricities of 12.5% and 25%, respectively), the acceleration responses of the upper structure increased in the overall frequency range in comparison with non-eccentric models. In the overall frequency range, increasing eccentricity leads to a more than 40% increase in acceleration response compared with the non-eccentric case. However, in the frequency range around 3 Hz and 4 Hz, as eccentricity increases, acceleration response can increase by up to approximately 100%. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Technical Variables** & **Values** & \\ \hline Size [m] & & 4.0 \(\times\) 4.0 & \\ \hline Max Loading (Force/Moment) & & 300 kN/1200 kN-m & \\ \hline Frequency Range (Hz) & & 0.1–60 & \\ \hline Control Axes & & 6 DOF & \\ \hline \multirow{2}{*}{Acceleration at Full Payload (g)} & X & Y & Z \\ \cline{2-3}  & 1.2 & 1.2 & 0.8 \\ \hline \multirow{2}{*}{Maximum Stroke (mm)} & X & Y & Z \\ \cline{2-3}  & \(\pm\)300 & \(\pm\)200 & \(\pm\)150 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Technical specification for the 3-D shaking table. Figure 14: Effect of base isolation on acceleration responses (0.3 g, EW). This behavior is attributed to the combined effects of eccentricity-induced torsional behavior and the fact that the earthquake excitation input has the highest energy content at around 10 Hz. This results in a significant increase in acceleration response in the range of 4 Hz to 15 Hz for the Ecc2 case. Table 8 compares the seismic acceleration responses of the base-isolated upper structure (dummy mass) for three models: non-eccentric (Con), eccentricity of 12.5% (Ecc1), and eccentricity of 25% (Ecc2).