## 1 Introduction  
The seismic behavior for liquid storage tanks on soil foundation is still an extremely significant engineering design index due to abundant periodic components of earthquake waves. The storage tanks are subjected to hydrodynamic pressures during horizontal seismic excitation which can exert great influences on the superstructure [1]. The hydrodynamic pressures generated by the resonant sloshing of the free surface can induce serious damage to the tank structures, for instance, splashing and overflowing of the liquid may occur, which can even cause explosions, fires and environmental pollution. Therefore, liquid sloshing is a fundamental issue in storage containers undergoing seismic loads [2]. [PERSON] [3] obtained a formulation of eigenvalue problem for a circular cylindrical shell partially filled with incompressible sloshing fluid. By using an isogeometric scaled boundary finite element technique, [PERSON] et al. [4] conducted parameter analysis on the effects of the shape and size of internal bodies in a circular tank on fundamental frequencies and sloshing forces. Considering fluid-structure interaction, [PERSON] and [PERSON] [5] investigated the dynamic response of a rectangular tank undergoing three-directional seismic ground motion whose directionality can influence the hydrodynamic pressure. [PERSON] [6] proposeda famous mass-spring model to illustrate the continuous liquid in cylindrical tanks. [PERSON] et al. [7] mainly focused on the differences in sloshing wave kinematics and dynamics for the same volume of liquid in storage vessels with various shapes by using the open source code OpenFOAM. A great deal of efforts are devoted to the sloshing dynamics and pressure distribution for liquid storage containers; however, much less attention is paid to the anti-sloshing problem for the storage vessels in the investigation [7]. Actually, internal structures such as annular or vertical baffles can be positioned in storage tanks to diminish the free sloshing [8; 9]. [PERSON] et al. [10] obtained sloshing mitigation numerically in a rectangular container with baffle with satisfactory accuracy. [PERSON] et al. [11] performed a series of numerical investigations on liquid responses in baffled containers. [PERSON] et al. [12] conducted the numerical analysis to obtain sloshing in a container equipped with a T-shaped baffle, showing that the existence of the annular baffle is highly effective to decrease sloshing forces. However, the applications of numerical approaches may face restrictions as a result of the ineffective grid generation technology for moving boundaries and complicated structure configurations. [PERSON] et al. [13] utilized experiment investigation to analyze the seismic responses of a cylindrical container with ring baffles. [PERSON] et al. [14] performed an experimental analysis for vertical slat screen influences on decreasing sloshing in a storage container. [PERSON] et al. [15] employed experiments to analyze inhibitory impacts of various kinds of vertical baffles on the hydrodynamic pressure. Nevertheless, it is almost impractical to conduct experiment studies on sloshing of liquid in tanks with multiple various baffles when combined with other complex systems that may need large amounts of tests. Compared with the existing numerical and experimental investigations, the theoretical method is more suitable to obtain parameter analysis for slight liquid sloshing. In terms of the analytical methods for the sloshing problems of storage containers, [PERSON] et al. [16] obtained an analytical result for the resonant frequency of sloshing in a container with perforated baffles. [PERSON] et al. [17; 18] utilized the subdomain partition method for liquid sloshing to perform parameter studies on dynamic characteristics and seismic responses of cylindrical tanks with multiple annular baffles while providing a small calculation and high accuracy. By employing the same approach, [PERSON] et al. [19] obtained the dynamics in a rectangular storage tank with a horizontal baffle.