Nonlinear Responses of Sloshing in Rectangular Tanks : 1st Report, Nonlinear Responses of Surface Elevation

Abstract

An analytical solution to represent the nonlinear responses of sloshing in a rectangular tank is obtained, in which the perturbation method is used, under the assumption of potential flow for the liquid, and it is compared with experiments. As the result, the following are found. When the depth of liquid in the tank is deeper than a certain value which is determined by the ratio of depth and width of the tank, then the surface elevation shows nonlinear response curves with softening restoring force characteristics. When the depth becomes shallower than that value, it shows nonlinear response curves with hardening ones. In deeper cases, the analytical solution is in good agreement with experiments. In shallower ones, it represents the qualitative characteristics of actual nonlinear sloshing. In the lower forcing frequency range, it deviates from the experimental values, but the linear solution is in good agreement with them in this range.