Generalized nonlinear modal model of the third order of smallness for sloshing in co-axial conical containers

Abstract

For the problem on the resonant sloshing in coaxial conical reservoirs occurring due to harmonic horizontal tank excitations, an infinite-dimensional governing system of third-oder ordinary differential equations is derived. The derivation scheme is based on the non-conformal mapping technique and the Moiseev–Narimanov asymptotics.