Nonlinear Vibrations in an Elastic Structure Subjected to Vertical Excitation and Coupled with Liquid Sloshing in a Rectangular Tank. 1st Report. Variations of Resonance Curves due to the Liquid Depth.

Abstract

The nonlinear coupled vibrations in an elastic structure and liquid sloshing in a rectangular tank are investigated. The tank has a free surface and the structure supporting it is vertically subjected to a sinusoidal excitation. In the theoretical analysis, the resonance curves for the responses of the structure and liquid surface are presented by the approximate method, when the natural frequency of the structure is equal to twice the natural frequency of one of the sloshing modes. From the theoretical analysis, we have obtained the following results: (a) Due to the nonlinearity of the fluid force, harmonic oscillations appear in the structure, while subharmonic oscillations occur on the liquid surface, (b) the shapes of the resonance curves change markedly depending on the liquid depth, and (c) the resonance curves for an arbitrary excited sloshing mode can be easily obtained by merely changing the dimensions of the tank such as the length and the width in the theoretical equations for the first sloshing mode. These results were qualitatively in good agreement with the experimental results obtained from having used water as the liquid.