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Random Excitation of a Structure Interacting With Liquid Sloshing Dynamics

[+] Author Affiliations
Takashi Ikeda

Shimane University, Matsue, Japan

Raouf A. Ibrahim

Wayne State University, Detroit, MI

Paper No. IMECE2002-32934, pp. 1363-1374; 12 pages
  • ASME 2002 International Mechanical Engineering Congress and Exposition
  • 5th International Symposium on Fluid Structure Interaction, Aeroelasticity, and Flow Induced Vibration and Noise
  • New Orleans, Louisiana, USA, November 17–22, 2002
  • Conference Sponsors: Applied Mechanics Division
  • ISBN: 0-7918-3659-2 | eISBN: 0-7918-1691-5, 0-7918-1692-3, 0-7918-1693-1
  • Copyright © 2002 by ASME


The nonlinear random interaction of an elastic structure with liquid sloshing dynamics in a cylindrical tank is investigated in the neighborhood of 1:2 internal resonance. Such internal resonance takes place when the natural frequency of the elastic structure is close to twice the natural frequency of the antisymmetric sloshing mode (1,1). The excitation is generated from the response of a linear shaping filter subjected to a Gaussian white noise. The analytical model involves three sloshing modes; (1,1), (0,1) and (2,1). The system response statistics and stability boundaries are numerically estimated using Monte Carlo simulation. The influence of the excitation center frequency, its bandwidth, and the liquid level on the system responses is studied. It is found that there is an irregular energy exchange between the structure and the liquid free surface motion when the center frequency is close to the structure natural frequency. Depending on the excitation power spectral density, the liquid free surface experiences zero motion, uncertain motion (intermittency), partially developed motion, and fully developed random motion. The structure response probability density function is almost Gaussian, while the liquid elevation deviates from normality. The unstable region, where the liquid motion occurs, becomes wider as the excitation intensity increases or as the bandwidth decreases. As the liquid depth decreases, the region of nonlinear interaction shrinks which is associated with a shift of the peak of the structure mean square response toward the left side of the frequency axis.

Copyright © 2002 by ASME



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