Asymmetric bifurcations in a pressurised circular thin plate under initial tension

Ciprian D. Coman

doi:10.1016/j.mechrescom.2012.09.005

Asymmetric bifurcations in a pressurised circular thin plate under initial tension

Ciprian D. Coman

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

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 language	English
Pages (from-to)	11-17
Number of pages	7
Journal	Mechanics Research Communications
Volume	47
Early online date	22 Oct 2012
DOIs	https://doi.org/10.1016/j.mechrescom.2012.09.005
Publication status	Published - Jan 2013
Externally published	Yes

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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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N2 - 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.

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.

KW - Asymmetric bifurcations

KW - Elastic stability

KW - Localised eigenmodes

KW - Thin plates

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VL - 47

SP - 11

EP - 17

JO - Mechanics Research Communications

JF - Mechanics Research Communications

SN - 0093-6413

ER -

Asymmetric bifurcations in a pressurised circular thin plate under initial tension

Abstract

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