Damped steady-state resonant sloshing in a container of circular cross-section for arbitrary periodic nonparametric forcing

Abstract

Nonlinear modal Narimanov-Moiseev—type equations are investigated to study resonant sloshing in a vertical cylindrical tank. The tank moves periodically in the space with the forcing frequency close to the lowest natural sloshing frequency. We show that the considered sloshing problem can to within the higher-order asymptotic terms be reduced to the case of orbital tank motions in the horizontal plane. Analytical solutions of the secular system which couples the dominant amplitudes of the steady-state sloshing are analytically solved. Effect of viscous damping is accounted. The results are compared with experimental measurements conducted by diverse authors for longitudinal and circular orbital tank excitations. A parametric analysis of the amplitude curves is done to clarify how the steady-state wave regimes and their stability change versus the forcing frequency and the semi-axes ratio of the elliptic orbit. The main result consists of confirming the experimental disappearance of the counter-directed swirling wave mode (relative to the elliptic orbit direction) when passaging to the circular orbit.