MODAL MODELLING OF THE NONLINEAR RESONANT FLUID SLOSHING IN A RECTANGULAR TANK I: A SINGLE-DOMINANT MODEL

Abstract

Steady-state nonlinear resonant fluid sloshing in moving tanks can be characterized by a finite set of natural modes (leading modes). Approximate solutions of the original free boundary value problem can be found from a system of nonlinear ordinary differential equations (modal system) coupling time-dependent amplitudes of these leading modes. The derivation of the modal systems combines projective and asymptotic methods. The work presents an extensive survey of the literature and examines bifurcations of periodic (steady-state) solutions of the single-dominant modal system based on Moiseyev asymptotic ordering. It describes two-dimensional resonant fluid sloshing in a rectangular tank due to its horizontal harmonic oscillations. The periodicity condition yields a two-point boundary value problem that allows both asymptotic and numerical treatments within the framework of the perturbed bifurcation theory. A secondary bifurcation that is found for response curves shows the flaws of the single-dominant modal modelling. Modifications of the single-dominant model should account for internal (secondary) resonance in the mechanical system leading to amplification of higher modes. Part II will consider modal systems which take into account the internal resonance.