NONLINEAR PARAMETRIC VIBRATIONS OF AN ELASTIC STRUCTURE WITH A CYLINDRICAL LIQUID CONTAINER (IN THE CASE OF AN ANTI-SYMMETRIC SLOSHING MODE)

摘要

The nonlinear-coupled vibrations of an elastic structure and liquid sloshing in a cylindrical container are investigated. Since the structure is vertically subjected to a sinusoidal excitation, the behavior of the liquid surface is governed by a kind of the Mathieu equation. Modal equations governing the coupled motions are derived, when the natural frequency of the structure is equal to twice the natural frequency of an anti-symmetric mode of sloshing. The theoretical resonance curves are also presented by using an FFT analysis and the improved harmonic balance method. The influences of a liquid level and a detuning parameter on the theoretical resonance curves are shown. A small deviation of the tuning condition can cause amplitude-modulated motions and separate the occurrence region of the coupled vibration into two regions. In the experiments, the theoretical resonance curves were qualitatively in agreement with the experimental data. In addition, amplitude-modulated motions were observed.