###### Abstract  
Sloshing in liquid storage tanks is a critical phenomenon that affects the stability, performance, and safety of various engineering systems, including fuel tanks, offshore structures, and industrial storage units. The presence of internal structures, such as vertical baffles, significantly influences the natural sloshing frequencies and fluid motion. However, existing theoretical models often rely on simplified assumptions that restrict their capacity to capture the complexities of fluid-structure interactions in baffled tanks. This study integrates the coupled Eulerian-Lagrangian method with the impulse excitation technique to predict natural sloshing frequencies in a rectangular tank with vertical baffles. By analyzing the system's response to an impulse excitation, we extracted the dominant sloshing frequencies while considering the impact of baffles on fluid dynamics. This computational approach provides a more realistic representation of sloshing phenomena and enables a parametric analysis of how various tank dimensions, fluid properties, and baffle configurations influence sloshing behavior. The findings of this study contribute to the improved design and optimization of liquid storage tanks, ensuring enhanced stability and performance in practical engineering applications. The integration of impulse excitation with the coupled Eulerian-Lagrangian method marks a significant advancement in sloshing analysis, offering a robust framework for understanding and mitigating the effects of sloshing in baffled tanks. s 2  
especially those with internal structures such as vertical baffles, which significantly affect sloshing frequencies and fluid motion. Among various internal structures affecting sloshing dynamics, vertical baffles are particularly influential due to their damping and flow-altering effects. They are commonly installed in industrial tanks to mitigate excessive sloshing, enhance liquid mixing, and prevent the formation of high-amplitude waves. Baffles influence the fluid's dynamic response by modifying flow patterns and increasing damping effects. Various studies have investigated the role of vertical baffles in sloshing mitigation. [PERSON] and [PERSON] (2006) examined sloshing loads in a moving, partially filled rectangular tank using both numerical and experimental approaches, employing the volume-of-fluid (VOF) method and validating the results against experimental data [10]. [PERSON] and [PERSON] (2009) explored sloshing suppression by vertical baffles using a virtual boundary force method and highlighted their effectiveness in reducing fluid motion [11]. [PERSON] et al. (2021) studied the impact of single and double vertical baffles on violent sloshing, emphasizing the importance of baffle arrangement in enhancing damping by measuring liquid elevation, energy dissipation, and impact pressures [12]. [PERSON] et al. (2012) analyzed the effect of baffle height on liquid sloshing in a laterally oscillating, three-dimensional rectangular tank, showing that higher baffles weaken vortex structures at their tips and thus influence the damping effect [13]. In addition to the structural effects of baffles, recent studies have emphasized that bubble or cavity formation during sloshing can significantly influence nonlinear fluid behavior. The formation of bubbles introduces complex fluid-structure interactions that alter the dynamic response beyond the predictions of linear theory. [PERSON] et al. (2024) demonstrated through numerical simulations that gas inflow into dual liquid tanks intensifies sloshing behavior and increases impact forces on tank walls [14]. [PERSON] et al. (2023) validated computational models capable of capturing detailed sloshing dynamics, including bubble formation and violent surface breakup, and showed good agreement with experimental observations [15]. Despite the practical significance of baffles, the impact of internal structures on natural sloshing frequencies remains insufficiently understood, and only a limited number of theoretical models predict these effects.