Hydroelastic Solution of the Sloshing of a Liquid in a Cylindrical Tank

Abstract

The problem of sloshing (free surface oscillations) of a liquid in a cylindrical tank with rigid walls and a flexible bottom (a thin elastic plate) is studied for both the axisymmetric and asymmetric cases. The coupled boundary-value problem of the liquid and the elastic bottom is solved for small motions. The frequency equations are obtained and the effect of the coupling investigated. It is shown that the frequency equations reduce properly to the various limiting cases. The orthogonality of the coupled mode shapes is investigated and a theorem concerning the coupled mode shapes is proved.