NONLINEAR VIBRATIONS OF ELASTIC STRUCTURES CARRYING TWO RECTANGULAR LIQUID-FILLED TANKS UNDER HORIZONTAL EXCITATION

摘要

Nonlinear vibrations of an elastic structure carrying two liquid-filled tanks under horizontal harmonic excitation are investigated. When a 1:1:1 ratio of internal resonance is satisfied among the natural frequencies of the structure and sloshing in the two liquid tanks, modal equations are derived by using Galerkin's method, taking into account the nonlinearity of the hydrodynamic force. Then, frequency response curves are calculated by using Andronov and Witt's method. Peculiar vibrations, referred to as 'multi-mode vibrations', sometimes may appear depending on the values of the system parameters. They never occur in a structure carrying only one liquid-filled tank. In other words, even if the dimensions of the two tanks are identical, the sloshing which occurs in each tank differs depending on the excitation frequency. The multi-mode vibrations include constant amplitude vibrations and amplitude modulated motion as well as chaotic vibrations.