Semi-analytical solution on three-layer liquid sloshing in the rectangular tank with bed topography

A suitable topography is useful for reducing the impact pressure and lateral loads of the layered liquid sloshing on the structure, which improves its stability and durability. Effect of the bed topography on the layered liquid sloshing in tanks is investigated analytically. The complex liquid domain is naturally decomposed into three subdomains due to the incompatibility of the three types of liquids. The boundary condition between the first liquid layer and the topography is derived. The topography can be considered as a trigonometric function in this study. The formal solution of each sub-domain is derived analytically by applying the separation of variables method. The characteristic equations are determined by substituting the formal solution into the interface boundary conditions and topographic boundary conditions. The dynamic response equation under lateral excitation can be further established. The present method is proved to match well with two other calculation results. The semi-analytic results show that the topography can considerably reduce multilayer liquid sloshing.