Effects of Higher Order Radial Modes upon Nonlinear Sloshing in a Circular Cylindrical Tank Subjected to Vertical Excitation

Abstract

Parametric vibration of the liquid surface in a partially filled circular cylindrical tank is investigated. The tank is subjected to horizontal, vertical and pitching excitations. Nonlinearity of the liquid surface oscillation is considered in the response analysis of the sloshing motion. The nonlinear and parametric ordinary differential equations, governing the axisymmetric liquid surface oscillation and including the higher order radial modes, are derived by applying Galerkin's method. It is confirmed that the vertical excitation causes the parametric excitation. In addition, it is noted that the pitching excitation also causes the parametric excitation when the pitching axis does not intersect the symmetrical axis of the circular cylindrical tank. The time histories of the liquid surface displacement to the harmonic vertical excitations are calculated in cases where the dominant mode is axisymmetric and where it has nodal radiuses. An experiment was conducted using a model tank. Good agreement was found between the theoretical and experimental results.