Asymmetric bifurcations in a pressurised circular thin plate under initial tension

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Abstract

It has been known for some time that under certain circumstances the axisymmetric solution describing the deformation experienced by a stretched circular thin plate or membrane under sufficiently strong normal pressure does not represent an energy-minimum configuration. By using the method of adjacent equilibrium a set of coordinate-free bifurcation equations is derived here by adopting the Föppl-von Kármán plate theory. A particular class of asymmetric bifurcation solutions is then investigated by reduction to a system of ordinary differential equations with variable coefficients. The localised character of the eigenmodes is confirmed numerically and we also look briefly at the role played by the background tension on this phenomenon.

Original languageEnglish
Pages (from-to)11-17
Number of pages7
JournalMechanics Research Communications
Volume47
Early online date22 Oct 2012
DOIs
Publication statusPublished - Jan 2013
Externally publishedYes

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plate theory
thin plates
Ordinary differential equations
differential equations
membranes
Membranes
coefficients
configurations
energy

Cite this

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abstract = "It has been known for some time that under certain circumstances the axisymmetric solution describing the deformation experienced by a stretched circular thin plate or membrane under sufficiently strong normal pressure does not represent an energy-minimum configuration. By using the method of adjacent equilibrium a set of coordinate-free bifurcation equations is derived here by adopting the F{\"o}ppl-von K{\'a}rm{\'a}n plate theory. A particular class of asymmetric bifurcation solutions is then investigated by reduction to a system of ordinary differential equations with variable coefficients. The localised character of the eigenmodes is confirmed numerically and we also look briefly at the role played by the background tension on this phenomenon.",
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Asymmetric bifurcations in a pressurised circular thin plate under initial tension. / Coman, Ciprian D.

In: Mechanics Research Communications, Vol. 47, 01.2013, p. 11-17.

Research output: Contribution to journalArticle

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AB - It has been known for some time that under certain circumstances the axisymmetric solution describing the deformation experienced by a stretched circular thin plate or membrane under sufficiently strong normal pressure does not represent an energy-minimum configuration. By using the method of adjacent equilibrium a set of coordinate-free bifurcation equations is derived here by adopting the Föppl-von Kármán plate theory. A particular class of asymmetric bifurcation solutions is then investigated by reduction to a system of ordinary differential equations with variable coefficients. The localised character of the eigenmodes is confirmed numerically and we also look briefly at the role played by the background tension on this phenomenon.

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KW - Elastic stability

KW - Localised eigenmodes

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