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Instability of sloshing motion in a vessel undergoing pivoted oscillations

Turner, MR, Alemi Ardakani, H and Bridges, TJ (2015) Instability of sloshing motion in a vessel undergoing pivoted oscillations Journal of Fluids and Structures.

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Abstract

Suspending a rectangular vessel partially filled with an inviscid fluid from a single rigid pivoting rod produces an interesting physical model for investigating the dynamic coupling between the fluid and vessel motion. The fluid motion is governed by the Euler equations relative to the moving frame of the vessel, and the vessel motion is given by a modified forced pendulum equation. The fully nonlinear, two-dimensional, equations of motion are derived and linearised for small-amplitude vessel and free-surface motions, and the natural frequencies of the system analysed. It is found that the linear problem exhibits an unstable solution if the rod length is shorter than a critical length which depends on the length of the vessel, the fluid height and the ratio of the fluid and vessel masses. In addition, we identify the existence of 1:1 resonances in the system where the symmetric sloshing modes oscillate with the same frequency as the coupled fluid/vessel motion. The implications of instability and resonance on the nonlinear problem are also briefly discussed.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Turner, MRUNSPECIFIEDUNSPECIFIED
Alemi Ardakani, HUNSPECIFIEDUNSPECIFIED
Bridges, TJUNSPECIFIEDUNSPECIFIED
Date : 1 January 2015
Identification Number : 10.1016/j.jfluidstructs.2014.10.012
Additional Information : NOTICE: this is the author’s version of a work that was accepted for publication inJournal of Fluids and Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Fluids and Structures, 52, January 2015, DOI 10.1016/j.jfluidstructs.2014.10.012
Depositing User : Symplectic Elements
Date Deposited : 17 Feb 2015 11:54
Last Modified : 17 Feb 2015 14:33
URI: http://epubs.surrey.ac.uk/id/eprint/807033

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