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Nonlinear energy transfer between fluid sloshing and vessel motion

Published online by Cambridge University Press:  19 February 2013

M. R. Turner  and
T. J. Bridges
M. R. Turner*
Affiliation:
Department of Mathematics, University of Surrey, Guildford GU2 7XH, UK
T. J. Bridges
Affiliation:
Department of Mathematics, University of Surrey, Guildford GU2 7XH, UK
*
†Email address for correspondence: M.Turner@surrey.ac.uk
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Abstract

This paper examines the dynamic coupling between a sloshing fluid and the motion of the vessel containing the fluid. A mechanism is identified that leads to an energy exchange between the vessel dynamics and fluid motion. It is based on a 1:1 resonance in the linearized equations, but nonlinearity is essential for the energy transfer. For definiteness, the theory is developed for Cooker’s pendulous sloshing experiment. The vessel has a rectangular cross-section, is partially filled with a fluid and is suspended by two cables. A nonlinear normal form is derived close to an internal 1:1 resonance, with the energy transfer manifested by a heteroclinic connection, which connects the purely symmetric sloshing modes to the purely antisymmetric sloshing modes. Parameter values where this pure energy transfer occurs are identified. In practice, this energy transfer can lead to sloshing-induced destabilization of fluid-carrying vessels.

JFM classification

Mathematical Foundations: General fluid mechanics Mathematical Foundations: Mathematical Foundations Mathematical Foundations: Variational methods

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 719 , 25 March 2013 , pp. 606 - 636
Copyright
©2013 Cambridge University Press

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