## 6 Analysis Results  
This section presents the results of numerical simulations performed by applying a unit impulse with a 0.05 s rise time to the cases summarized in Figure 8. As shown in Figure 1, the surface elevation was measured at a location 0.02 m away from the tank wall. The results from the 15 s simulation generally indicate that as the number of baffles increases from one to two, or as the baffle height increases, the vibrations decay more quickly as shown in Figure 9. This suggests that baffles play a significant role in controlling sloshing vibrations, with their effect becoming more pronounced as baffle height increases. Figure 8: Analysis cases according to number and length of baffles. Figure 7: Comparison of Load A and B in the frequency domain. Figure 10 presents the frequency-domain results of the simulations, illustrating how the frequency characteristics vary depending on the number of baffles and their height. Specifically, the frequency response shapes remain similar for cases with two baffles at  
Figure 9: Time-domain responses for simulation cases. 50% height, but they begin to diverge once the baffle height exceeds 75%. This suggests that when the baffle height surpasses a certain threshold, its influence on fluid dynamics becomes nonlinear. Figure 10: Frequency-domain responses for simulation cases. Figure 11 summarizes the lowest natural sloshing frequencies for each case. The results indicate that as the number of vertical baffles increases and their height rises, the lowest natural sloshing frequency consistently decreases. However, the trend differs depending on the number of baffles. For a single baffle, a sharp decrease in the lowest natural frequency occurs at \(\frac{h_{b}}{h_{w}}=0.90\), whereas for two baffles, a significant drop is observed at a lower height ratio of \(\frac{h_{b}}{h_{w}}=0.75\). A quantitative analysis of the nonlinear frequency shift shows that while the frequency decreases nearly linearly for lower baffle heights (\(\frac{h_{b}}{h_{w}}\leq 0.50\)), significant nonlinear deviations emerge at higher baffle heights. For a single baffle, the frequency deviation from the expected linear trend reaches approximately 5.0% at \(\frac{h_{b}}{h_{w}}=0.75\) and increases sharply to about 20.8% at \(\frac{h_{b}}{h_{w}}=0.90\). Similarly, for two baffles, the deviations are about 20.0% and 24.1% at \(\frac{h_{b}}{h_{w}}=0.75\) and 0.90, respectively. These results quantitatively confirm that strong nonlinear effects arise when the baffle height exceeds approximately 75% of the water depth, especially in configurations with multiple baffles. Therefore, special attention must be paid when determining the natural sloshing frequencies of baffled tanks, as nonlinear effects can significantly alter the dynamic response. To validate the CEL-based calculations, a sloshing analysis was performed by applying the lowest natural frequencies summarized in Figure 11 to the target tank. The analysis was conducted for two cases: one with a single baffle at 50% height (see Figure 12a) and another with two baffles (see Figure 12b). The results show that a clear sloshing phenomenon was observed when the natural frequencies derived in this study were used for the analysis. As seen in Figure 4, for a tank without baffles, resonant phenomena were observed when the analysis was conducted using the natural frequencies calculated from the theoretical formula. We compared the result of this study with the closed-form equations for the natural sloshing frequency of a tank with vertical baffles, as introduced in Section 2.1 (specifically, the equations by [PERSON] et al. (2006) [16] and [PERSON] et al. (2018) [17]). To compare with the equation from [PERSON] et al. (2006) [16], we first calculated the effective fill-depth (\(h_{c}\)) based on the number and height of the baffles, and we then plotted the relationship between this effective fill-depth and the lowest natural sloshing frequency in Figure 13a. However, for comparison with the equation from [PERSON] et al.