The thesis considers transtiton from two-dimensional to three-dimensional response (swirling) in a problem of liquid sloshing in a symmetric vessel under external periodic forcing. Such transition is well-known in the vicinity of the primary 1:1 resonance between the lowest eigenfrequency of the sloshing mass, and the external force. The thesis analyzes the possibility to describe the transition by means of reduced-order dynamical model.
The suggested model comprises planary damped nonlinear oscillator with unidirectional forcing. The transition to the sloshing is associated with loss of stability of the one-dimensional response. Analysis by means of a multiple-scaple expansion allows mapping the transition threshold at the plane of parameters for given initil conditions. One reveals that common cubic nonlinearity is insufficient to match the available numeric and experimental results; more complicated cubic-fifth order model with combined softening and stiffening is required. The results are verified by means of direct numeric simulations that reveal additional response patterns, including the two-dimensional chaotic responses. Such responses were also observed in realistic sloshing systems.