Free and Forced Oscillations of a Liquid in an Axisymmetric Tank at Low-Gravity Environments

Abstract

This paper presents a procedure to analyze the free and forced liquid sloshing motions in an axisymmetric tank of arbitrary shape at low-gravity environments. The free-vibration problem is solved by extending the analysis of Satterlee and Reynolds for a circular cylindrical tank with a flat bottom. The forced-motion problem is solved by first expanding the velocity potential, the interface wave height, and the forcing functions in terms of the normal mode shapes obtained in the free-vibration analysis. The solutions hold for any arbitrary horizontal translational motion of the tank.