On internal resonances for sloshing in mobile coaxial reservoirs of conical shape

Abstract

Employing the secondary (internal) resonance condition for steady-state sloshing in a conical tank that appears due to resonant excitation of the lowest natural frequency, the paper establishes a set of input geometric parameters (semi-apex angle of outer and inner conus) for which the secondary resonance phenomenon can lead to amplification of higher modes. A series of recommendation regarding the forthcoming development of nonlinear modal methods for the indicated tank shape are formulated.