Nonlinear semi-analytical modeling of liquid sloshing in rectangular container with horizontal baffles

A nonlinear semi-analytical scheme is proposed for investigating the finite-amplitude nonlinear sloshing in a horizontally baffled rectangular liquid container under the seismic excitation. The sub-domain method is developed to analytically derive the modal behaviors of the baffled linear sloshing. The viscosity dissipation effects from the interior liquid and boundary layers are considered. With the introduction of the generalized time-dependent coordinates, the surface wave elevation and velocity potential are represented by a series of linear modal eigenfunctions. The infinite-dimensional modal system of the nonlinear sloshing is formulated based on the Bateman-Luke variational principle, which is further reduced to the finite-dimensional modal system by using the Narimanov-Moiseev asymptotic ordering. The base force and overturning moment induced by the nonlinear sloshing are derived as the functions of the generalized time-dependent coordinates. The present results match well with the available analytical, numerical, and experimental results. The paper examines the surface wave elevation, base force, and overturning moment versus the baffle parameters and excitation amplitude in detail.