Experiments on the periodic oscillation of free containers driven by liquid sloshing

Abstract

AbstractExperiments on the time-periodic liquid sloshing-induced sideways motion of containers are presented. The measurements are compared with finite-depth potential theory developed from standard normal mode representations for rectangular boxes, upright cylinders, wedges and cones of$9{0}^{\ensuremath{\circ} } $apex angles, and cylindrical annuli. It is assumed that the rectilinear horizontal motion of the containers is frictionless. The study focuses on measurements of the horizontal oscillations of these containers arising solely from the liquid waves excited within. While the wedge and cone exhibit only one mode of oscillation, the boxes, cylinders and annuli have an infinite number of modes. For the boxes, cylinders and one of the annuli, we have been able to excite motion and record data for both the first and second modes of oscillation. Frequencies$\omega $were acquired as the average of three experimental determinations for every filling of mass$m$in the dry containers of mass${m}_{0} $. Measurements of the dimensionless frequencies$\omega / {\omega }_{R} $over a range of dimensionless liquid masses$M= m/ {m}_{0} $are found to be in essential agreement with theoretical predictions. The frequencies${\omega }_{R} $used for normalization arise naturally in the mathematical analysis, different for each geometry considered. Free surface waveforms for a box, a cylinder, the wedge and the cone are compared at a fixed value of$M$.