Damped resonant steady-state sloshing in an upright circular tank

Abstract

The nonlinear Narimanov–Moiseev-type modal system with linear damping terms is employed to study the damped steady-state resonant sloshing in an upright circular tank. Estimating the damping coefficients (ratios) by using Miles’ formula shows that the damping may matter for laboratory tanks. An asymptotic steady-state solution of the modal system is derived for a prescribed cyclic tank motion with four (sway/surge/pitch/roll) degrees of freedom; the forcing frequency is close to the lowest natural sloshing frequency. The steady-state response curves by the two lowestorder natural sloshing mode amplitudes are examined versus the semi-axes ratio of the artificial elliptic orbit.