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Special Section: Computational Fluid Mechanics and Fluid–Structure Interaction

Liquid Sloshing Damping in an Elastic Container

[+] Author and Article Information
Thomas Miras

ONERA, The French Aerospace Lab, BP 72, 92322 Chatillon Cedex, Francethomas.miras@onera.fr

Jean-Sébastien Schotté

ONERA, The French Aerospace Lab, BP 72, 92322 Chatillon Cedex, Franceschotte@onera.fr

Roger Ohayon

CNAM, Structural Mechanics and Coupled System Laboratory, 292 rue Saint Martin, Paris, 75141 Franceroger.ohayon@cnam.fr

In Ref. 10, Morand and Ohayon also propose to use ϕ, the solution of the hydroelastic problem without gravity.

Let α be the algebraic multiplicity of the eigenvalue pi, α is the order of the corresponding zero in det(P(p)). The geometric multiplicity β of pi is the dimension of the associated characteristic subspace. For a semisimple eigenvalue we have: α=β.

J. Appl. Mech 79(1), 010902 (Dec 13, 2011) (8 pages) doi:10.1115/1.4005189 History: Received May 05, 2011; Revised August 25, 2011; Published December 13, 2011; Online December 13, 2011

It is proposed to investigate in this paper the damped vibrations of an incompressible liquid contained in a deformable tank. A linearized formulation describing the small movements of the system is presented. At first, a diagonal damping is introduced in the reduced equations of the hydroelastic sloshing problem. We obtain a nonclassically damped coupled system with a damping matrix that is not symmetric. Then, by projecting the system onto its complex modes, the frequency and time responses for different type of loads are built. A numerical application is illustrated on a test case.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Description of the system and notations

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Figure 2

Example of a sloshing mode

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Figure 6

Snapshots of the liquid deformation at different instants for a harmonic excitation at the frequency 0.99 Hz (black arrow in Fig. 6). The colors represent the pressure fluctuations in the fluid.

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Figure 5

Time response of point A in the radial direction for a harmonic excitation at the frequency f1  = 0.63 Hz and a Heavyside; F0  = 600 N

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Figure 4

Comparison between the frequency responses in displacement of the point A from 0 to 6 Hz in the radial direction for an excitation at the same point and in the same direction

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Figure 3

Test tank. Height: 2 m, Radius: 2 m.

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