230 Nonlinear Vibrations of Elastic Structures with a Square Liquid Tank Subjected to Vertical Excitation

Abstract

Nonlinear vibrations of an elastic structure, with a nearly square liquid tank, under vertical harmonic excitation are investigated. When the tuning condition, a ratio 2:1:1, is satisfied among the natural frequencies of the structure and two sloshing modes (1, 0) and (0, 1), the equation of motion for the structure and the modal equations for sloshing are derived considering the nonlinearity of sloshing. Then, van der Pol's method is employed to determine the frequency response curves. The effectiveness of a square liquid tank as a tuned liquid damper is shown by investigating the influences of the system parameters on the frequency response curves.