Case Study on Combination Resonance of Liquid Sloshing Under Multiple Excitations

Abstract

Liquid sloshing problem in liquid-filled container under excitation is important in engineering field. When the resonant conditions are met, resonances of different types occur, which will lead to unexpected sloshing behaviors. To explore the fundamentals of the resonances in sloshing dynamics, the study is carried out. In this work, analytical analysis is approached. The nonlinear governing equations of the liquid sloshing modals in cylindrical boundary basin under multi-frequency excitations are adopted and then established. By means of multi-scale method, the possible combinations of frequencies which will cause resonances are found. Two general cases of single combination resonance and hybrid combination resonance are investigated analytically. The bifurcation equations of the sloshing problem are got analytically and the results show that in single combination resonance mode, the frequency curve merges hard spring characteristic and with the bifurcation parameters varying, the qualitative results would not change. While in hybrid combination resonance case, the behaviors are more complex. Seven non-trial solutions exist at the same time. The case studies show that adequate dynamical behaviors exist in sloshing problem when resonances occur. And varied resonant conditions can be achieved when system is disturbed by different frequency components. The results enrich the exploration of the dynamical analysis of the liquid sloshing problem and provide theoretical basis for system design and optimization.