This paper describes the development of a new efficient semi-analytical method, namely scaled boundary finite-element method (SBFEM) for the analysis of sloshing in axi-symmetric vessels based on multimodal analysis, and the governing Laplace equations and linear free surface boundary condition are also applied to the proposed model. A two dimensional eigenvalue problem is obtained by using the scaled boundary finite element method for zero external excitation, which is solved through a variational (Garlerkin) formulation that uses three node finite elements by only discreting the boundary of the water surface and walls, then the dimension of the problem is reduced by one. Subsequently, based on an appropriate decomposition of the container fluid motion, and considering the eigenmodes of the corresponding eigenvalue problem, an efficient methodology is proposed for externally-induced sloshing, through the calculation of the corresponding sloshing (or convective) masses. Numerical results are obtained for sloshing frequencies and masses in spherical vessels and a conical vessel, and the dynamic response of the sloshing is also obtained under different seismic waves. The numerical results are in very good comparison with other analytical or numerical solutions.

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