Sloshing response of nonuniform density liquid in a laterally excited tank

摘要

A study on the sloshing response of nonuniform density liquid in a tank undergoing lateral base excitations is presented. The system considered is a circular cylindrical tank containing a liquid whose density increases with the liquid depth. The density distribution along the depth can be of any arbitrary continuous function. In the analysis, the liquid field is divided into n layers. The thicknesses of the liquid layers can be different, but the density of each liquid layer is considered to be uniform and its value is assigned to be the value of the original liquid density at the mid-height of that layer. The problem is solved by the transfer matrix technique. The effect of the nonuniform liquid density on the sloshing response is illustrated in a numerical example in which the linear and cosine distributions of the liquid density are assumed. The response functions examined include the sloshing frequencies, surface wave height, and the associated convective hydrodynamic pressure. The results are presented in tabular and graphical forms. It is found that the natural frequencies of the sloshing motion for nonuniform density liquid are lower than those of the uniform density liquid of the same total depth contained in an identical tank. Also, it is shown that for nonuniform density liquid, the maximum sloshing wave height may increase significantly and the magnitude of the convective hydrodynamic pressure may be quite different compared with that of a uniform liquid contained in an identical tank.