## 8 Conclusions  
This study introduced an integrated numerical framework for predicting natural sloshing frequencies in baffled rectangular tanks, combining the CEL method with the IET. The results demonstrate that vertical baffles significantly alter the fluid's dynamic behavior, primarily by reducing natural frequencies and introducing nonlinear flow features, particularly when the baffle height exceeds a critical threshold relative to water depth.  
This study also revealed that when the baffle height exceeds a certain threshold, the sloshing behavior exhibits nonlinear characteristics, leading to a significant shift in the frequency response. This nonlinearity is crucial for understanding the full range of sloshing behavior in baffled tanks, which is often not adequately captured by traditional theoretical models.  
Through a comparison with the closed-form equations developed by [PERSON] et al. (2006) [16] and [PERSON] et al. (2006) [17], this study demonstrated that with regard to the lowest natural sloshing frequency, the closed-form equations based on the potential theory can yield reasonable results when applied to tanks with vertical baffles. Also, the CEL-IET method proved to be a reliable framework for modeling and predicting sloshing behavior in complex tank geometries.  
Despite these contributions, this study has several limitations. The analysis was restricted to the fundamental mode; higher-order sloshing modes and their possible interactions with structural modes were not addressed. The tank and baffles were modeled as rigid structures, neglecting the effects of structural flexibility. In addition, only rectangular tank geometries were considered, whereas sloshing dynamics can vary considerably across different tank shapes and internal layouts.  
Furthermore, since the findings are based solely on numerical simulations, experimental validation is essential. Real-world factors such as fabrication tolerances, external disturbances, and measurement uncertainties must be accounted for to assess the practical applicability of the proposed method.  
Future research should therefore focus on the following areas:  
* Extending modal analysis to capture higher-order sloshing frequencies and their interactions;
* Implementing fully coupled fluid-structure interaction (FSI) modeling for flexible structures;
* Applying the method to a broader range of tank geometries and baffle configurations;
* Conducting experimental studies to validate and refine the simulation results.  
By addressing these aspects, the proposed framework can be further advanced into a predictive and generalizable tool for the design and safety evaluation of liquid-containing structures in marine, aerospace, automotive, and energy industries.  
Conceptualization, S.-H.P. and Y.I.P.; methodology, S.-H.P. and J.-H.K.; validation, S.-H.P.; formal analysis, T.Y.; investigation, T.Y.; writing--original draft preparation, S.-H.P.; writing--review and editing, J.-H.K. and Y.I.P.; visualization, S.-H.P.; supervision, Y.I.P.; project administration, Y.I.P.; funding acquisition, J.-H.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Dong-A University research fund.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.