Sloshing Effects in Half-Full Horizontal Cylindrical Vessels Under Longitudinal Excitation

A mathematical model is developed for sloshing effects in half-full horizontal cylindrical vessels, under external excitation in the direction of the longitudinal vessel axis. In this geometry the problem is not separable. The velocity potential is expressed in a double series form, and after some mathematical manipulation the problem results in a series of systems of ordinary linear differential equations, one for each longitudinal mode. For the particular case of harmonic motion, a semi-analytical solution is possible. Keeping only the first two terms of the expansion in the transverse direction, an elegant formulation of remarkable accuracy is obtained. Hydrodynamic pressures and forces are calculated for harmonic excitation and for a real seismic motion event. Finally, the equivalence between the half-full horizontal cylinder and an “equivalent” rectangle is demonstrated.