Multiple Internal Resonance in a Structure-Liquid System

Abstract

The autoparametric coupling of a vibrating structure with liquid sloshing modes is demonstrated by means of a system consisting of a two degree of freedom structure carrying a rigid container partially filled with liquid. When the system is subjected to vertical excitation the liquid container oscillates up and down and, under certain internal resonance condition, it moves laterally as well. Energy is then exchanged between the structure vibration modes and the liquid sloshing modes. Nonlinear inertia terms in the equations of motion predominate in the behavior of the system undergoing autoparametric resonance. For two simultaneous internal resonance relations and external resonance near one of the frequencies involved in the internal resonance relations, the system performance is investigated theoretically and experimentally. The system shows unsteadiness and instability for most of the conditions considered, and these unstable motions are demonstrated in the experimental investigation. The effects described must be regarded as possible sources of structural failure in practical engineering systems.