Nonlinear Vibrations of an Elastic Structure Subjected to Vertical Excitation and Coupled With Liquid Sloshing in a Cylindrical Tank: Resonance With an Axisymmetric Mode

Abstract

Abstract The nonlinear coupled vibrations of an elastic structure and liquid sloshing in a cylindrical tank are investigated. When the structure is vertically subjected to a sinusoidal excitation, and when the natural frequency of the structure is equal to twice the natural frequency of the first axisymmetric mode of sloshing, modal equations governing the coupled motions are derived. Then, the theoretical resonance curves are presented by using the method of harmonic balance and an FFT analysis. As a result, it is demonstrated that the resonance curve for the structure changes from a shape with a peak to a flat shape as the liquid level decreases. It is also clarified that amplitude-modulated motions appear when the tuning condition is deviated. In experiments, theoretical resonance curves were qualitatively in good agreement with the experimental results.