NONLINEAR VIBRATIONS IN A PARAMETRICALLY EXCITED FLUID-STRUCTURE INTERACTION SYSTEM WITH ONE-TO-ONE INTERNAL RESONANCE

摘要

Theoretical resonance curves prove that a structure's resonance can facilitate liquid sloshing even when the internal resonance ratio is one-to-one. An investigation of nonlinear sloshing liquid vibrations in a rectangular tank supported by an elastic structure that is subjected to a vertical and sinusoidal excitation reveals that liquid sloshing occurs when the structure's natural frequency is approximately equal to the natural frequency of sloshing, that is, in the state of one-to-one internal resonance, and that amplitude-modulated motions appear when the condition of the internal resonance deviates to some extent. A special consideration of the nonlinear inertia effects of liquid force and the use of Galerkin's method help derive the differential (modal) equations governing the dynamic behaviors of the fluid-structure interaction system, while van der Pol's method helps express the theoretical resonance curves. These theoretical results are in quantitative agreement with the experimental data.