# The Sloshing-Induced Motion of Free Containers

## Abstract

Experiments for the time-periodic liquid sloshing-induced sideways motion of free containers are compared with theory using standard normal mode representations for rectangular boxes, upright cylinders, wedges and cones of \(90^{\circ }\) apex angles, and cylindrical annuli. While the wedge and cone exhibit only one mode of oscillation, the boxes, cylinders and annuli have an infinite number of modes. In some cases we have been able to excite the second mode 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.

## Keywords

Apex Angle Transverse Oscillation Liquid Filling Large Cylinder Liquid Slosh## Notes

### Acknowledgments

We have benefitted greatly from discussions with Dr. Mark Cooker and Professor Jie Yu during all phases of the work. We appreciate the precision work of John Butler at Colorado Plastic Products, Inc. in fabricating the boxes and the wedge, and of James Tucker of Tucker Precision Machining for turning the cone on a lathe from solid stock. Michael Sprague provided guidance in programming Mathematica. We thank Yun Peng who assisted in taking videos of our experiments and in some of the measurements.

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