Abstract
In this paper, the three-dimensional nonlinear characteristics of multi-surface liquid motion in a rectangular tank are investigated. The rectangular tank is divided into two parts by the baffle, which is perpendicular to the bottom of the tank and does not reach the bottom. The liquid oscillation subject to the horizontal excitation parallel to the baffle is focused on. The nonlinear ordinary differential equations governing the liquid oscillation are derived by using the Galerkin method. The admissible functions are assumed to be combinations of the modal functions. The modal functions are obtained by the boundary element method. It is pointed that the two modes, one of which oscillates in phase on both sides of the baffle and another oscillates in anti-phase, appear. The nonlinear coupling characteristics of those two dominant modes are discussed. It is noted that the mode, which does not directly excited by the excitation, is parametrically excited by the directly excited mode and that the three-dimensional liquid surface oscillation occurs as a result of parametric resonance. Frequency responses are obtained by applying the shooting method to the derived equations and stability analysis is conducted. Experiments were conducted by using a model tank. The occurrence of three-dimensional liquid surface oscillation in the narrow frequency range near the natural frequencies of the in-phase mode and the anti-phase mode is confirmed in both analytical and experimental results. It is shown that the amplitude of the three-dimensional liquid surface oscillation is larger than that of two-dimensional liquid surface oscillation.
