Sloshing Modes in a Cuboidal Tank

This Demonstration shows the sloshing modes (, ) of a liquid in a partially filled rectangular tank with base .


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Starting from Laplace's equation in Cartesian coordinates, assume that the boundary and free-surface conditions are all equal to zero and that the solution is separable. Let be the height of the liquid when it is still. The solution at time is:
where is the frequency and the gravitational acceleration.
[1] P. Hagedorn and A. DasGupta, Vibrations and Waves in Continuous Mechanical Systems, Chichester, UK: John Wiley & Sons, 2007.
[2] J. Kobine. Sloshing in a Square Tank [Video]. (Jan 31, 2013) www.youtube.com/watch?v=Yh3FWtecWIc.
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