## 1 Introduction
It is worth noting that regarding rectangular liquid storage tanks under three-dimensional earthquake excitations, the corner of the tanks was found to be the critical location for sloshing [38]. Furthermore, it was found that increasing the pulse period can increase the maximum sloshing height of cylindrical liquid storage tanks [26]. [PERSON] and their colleagues studied a cylindrical liquid storage tank with a natural convective period of 5.42 s under 38 near-fault pulse-like earthquakes with pulse periods ranging from 1.5 to 8 s [26]. Dynamic responses of liquid storage tanks have also been shown to be highly sensitive to the characteristics of the applied loads. It has been shown that the pulse characteristics of ground motion increase dynamic pressures on the tanks' walls as well as dynamic loads [27; 39]. [PERSON] et al. studied the sloshing response of rectangular liquid storage tanks under earthquakes with different frequency contents [40]. Accordingly, they modeled six two-dimensional liquid storage tanks, including squat, square, and slender tanks, with different water height to tank length ratios. According to their findings, the maximum sloshing response is highly sensitive to earthquake records with high-frequency contents. [PERSON] et al. demonstrated the importance of considering higher sloshing modes when calculating the maximum linear sloshing [41]. The higher sloshing modes have, therefore, been considered in more recent studies of the seismic behavior of liquid storage tanks. For example, [PERSON] et al. considered the first three convective modes to calculate the maximum sloshing wave height [42]. It is worth mentioning that most design codes, except NZSEE [43], ignore the effect of higher convective modes on the maximum sloshing response. In the case of rectangular liquid storage tanks under multi-directional earthquake ground motions, little research has been conducted on the effects of seismic wave incidences on the seismic response of liquid storage tanks [44]. [PERSON] et al. studied the effect of incident angle on the maximum force on a rigid rectangular tank under unidirectional harmonic and seismic loads [45]. Under both types of loads, the direction of motion parallel to the tank walls induced the maximum load in the tank. The effects of incident angle have been shown to affect both convective and impulsive responses. [PERSON] and his colleague studied the effects of incident angle on the behavior of a rectangular liquid storage tank with a planar aspect ratio of 3 under a far-fault three directional ground motion by rotating the horizontal earthquake components from 0 to 170 degrees with 10-degree increments [46]. They found that the impulsive and convective responses of the tank are greatly affected by changing the incident angle. The effects of incident angle on the convective and impulsive responses of a concrete liquid storage tank were studied by [47]. In the presence of seven different incident angles, both the convective and impulsive responses of the liquid storage tank were found to be sensitive to angle variations. It has been demonstrated by [47] that the angle of incidence of input ground motions greatly affects the seismic response of rectangular liquid storage tanks. According to that study of rectangular liquid storage tanks with three different planar aspect ratios, structural displacement is related to the sloshing response, such that the sloshing height increases when the structural displacement decreases with a change in the angle of incidence. Various methods have been employed in the literature to study the impact of the parameters mentioned above on liquid storage tanks' dynamic behavior. Among these methods, numerical methods are widely used to study this behavior. As a part of the research conducted by [PERSON], the Lagrangian principle and the Hamiltonian formulation for water waves were extended to three-dimensional problems of nonlinear water waves in hydrodynamic interaction with floating bodies [48].