Response of half–full horizontal cylinders under transverse excitation

Abstract

The present work investigates the response of half–full horizontal cylindrical vessels under external excitation in the transverse direction. A two dimensional mathematical model is developed to describe sloshing effects in rigid vessels. The velocity potential is expressed in a series form, where each term is the product of a time function and the associated spatial function. In this geometrical configuration the spatial functions are not orthogonal and the problem is not separable. Application of the boundary conditions results in a system of ordinary linear differential equations, which are solved numerically. Sloshing frequencies of half–full horizontal cylinders are computed, and hydrodynamic forces are calculated. Under harmonic excitation, the formulation results in a system of linear equations, allowing for a semi-analytical solution. A simplified version of the mathematical model is also developed, which considers the first two terms of the series and results in an elegant solution. Furthermore, assuming a beam-type deformation of the container, the simplified formulation can be extended to approximate the coupled response of the container-liquid system. Using this formulation, the response of a typical pressure vessel under ground-motion excitation is calculated and the effects of wall deformation are demonstrated.