A two-dimensional semi-analytic solution on two-layered liquid sloshing in a rectangular tank with a horizontal elastic baffle

A semi-analytic study on two-layered liquid sloshing in a horizontal excited two-dimensional rectangular tank with a horizontal elastic baffle was performed. The present work is a further development of the semi-analytical technique for solving the single-layer liquid sloshing problem. The horizontal elastic baffle was located in the lower liquid or upper liquid. First, the complex liquid domain in a baffled tank was divided into several simple sub-domains to solve the analytic solution. The wet mode of a horizontal baffle was presented according to the Eulerian Bernoulli beam. The continuity boundary condition on the interfaces between two liquids and the virtual interfaces was given. Then, the formal solution was derived for each sub-domain and a horizontal baffle using the superposition principle and the method of separation of variables. Then, the total velocity potential subject to lateral excitation was summed over the container potential function and the liquid disturbance potential. The dynamic response equation for two-layered liquid sloshing was established. Multiple methods verified the semi-analytic solution's correctness and agreed well with other methods. Finally, the numerical analysis mainly shows that the density ratio becomes more significant for the coupled frequency when the baffle is in the upper liquid. A large baffle's width suppresses the liquid flow in the baffled tank effectively. Furthermore, adjusting the baffle and the layered liquid parameters can significantly suppress layered liquid sloshing. For the seismic response, the elevation energy is mainly located after 2.5 s.