###### Abstract
[PERSON] et al. (2006) analyzed the natural frequencies of sloshing in prismatic tanks with bottom baffles, employing a variational method and introducing the concept of effective liquid fill-depth to modify traditional frequency estimations [16]. [PERSON] et al. (2018) extended this analysis by using a boundary element method (BEM) to study natural frequencies and mode shapes in two-dimensional baffled tanks, proposing empirical formulas for sloshing frequency prediction [17]. However, these analytical approaches generally assume linear fluid motion and two-dimensional simplifications, limiting their ability to capture three-dimensional and nonlinear behaviors in baffled tanks. To address these limitations, advanced computational techniques have been increasingly adopted. In particular, the coupled Eulerian-Lagrangian (CEL) method has emerged as a powerful tool for modeling fluid-structure interactions (FSIs) and capturing the complex dynamics of sloshing phenomena [18]. The CEL method treats the fluid domain using a fixed Eulerian mesh while modeling solid structures, such as tank walls and baffles, with a moving Lagrangian mesh. This dual approach enables accurate simulation of large free surface deformations, flow separation, and vortex generation around internal structures, making it particularly suitable for analyzing sloshing in baffled tanks. To further enhance the accuracy of natural frequency prediction, this study integrates the impulse excitation technique (IET), a well-established experimental method, into the numerical framework. The IET involves applying a brief, high-intensity impulse to the system and analyzing the resulting dynamic response to extract natural frequencies. Itis particularly effective for identifying resonance peaks within the frequency spectrum, offering a clear and robust means of characterizing dynamic behavior [19; 20]. In this study, we integrated the IET into a CEL-based finite element model to achieve accurate predictions of natural sloshing frequencies in a rectangular tank equipped with vertical baffles. By simulating the tank's response to impulse excitation, we extracted the natural frequencies while explicitly accounting for the dynamic modifications introduced by baffles. This computational approach not only improves the realism of sloshing modeling but also enables systematic parametric studies to investigate the influence of various tank dimensions, fluid properties, and internal configurations on sloshing frequencies. While existing analytical models rely on simplifying assumptions that often neglect detailed fluid-structure interactions, the present approach provides a more comprehensive and accurate analysis of sloshing dynamics. The integration of impulse excitation with the CEL technique represents a significant advancement in the numerical modeling of sloshing phenomena, offering a robust framework for understanding the influence of baffles on natural sloshing behavior. This study focused on the lowest natural sloshing frequency because it typically governs the dominant dynamic response of liquid-filled tanks and is most critical for ensuring structural stability and avoiding resonance in practical engineering applications. This focus aligns with established practices in sloshing research, where the first mode often contributes the largest amplitude and energy. Nonetheless, it is acknowledged that higher-order modes can become important in certain scenarios, such as in large tanks, tanks with complex internal structures, or under high-frequency external excitations. A comprehensive analysis including higher modes remains an important direction for future research.