Nonlinear Vibrations of an Elastic Structure Subjected to Vertical Excitation and Coupled with Sloshing in a Rectangular Tank. 2nd Report. Influences of the Deviation of Tuning Condition on Resonance Curves.

Abstract

This paper deals with the nonlinear coupled-vibrations of an elastic structure and liquid sloshing in an attached rectangular tank. The structure is vertically subjected to a sinusoidal excitation. The natural frequencies of the structure and the liquid sloshing are in the ratio of two to one, which is called a tuning condition. Influence of a deviation of the tuning condition on the resonance curves is focused on. In the theoretical analysis, the following results were obtained : (a) the small deviation of the tuning condition leads to causing an almost periodic oscillation and a chaotic oscillation, (b) these oscillations appear for a negative detuning in high liquid levels, and a positive deviation in low liquid levels, and (c) the coupled vibrations can occur separately in two regions of excitation frequency when the comparatively large deviation exists. In experiments, the experimental resonance curves were in agreement with the theoretical results, and almost periodic oscillations were observed.