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Effects of exponentially small terms in the perturbation approach to localized buckling


Wadee, MK and Bassom, AP, Effects of exponentially small terms in the perturbation approach to localized buckling, Proceedings of the Royal Society of London A, 455, (1986) pp. 2351-2370. ISSN 1364-5021 (1999) [Refereed Article]

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The Royal Society

DOI: doi:10.1098/rspa.1999.0407


Localized buckling solutions are known to exist in the heuristic model of an elastic strut resting on an elastic (Winkler) foundation. The primary localized solution emerging from the critical buckling state consists of an amplitude envelope of approximately the form of a hyperbolic secant function which modulates a fast-varying sinusoidal oscillation. In previous works such solutions have been tracked for the entire post-buckling regime both numerically and through a Rayleigh-Ritz approach.

A very rich structure is known to exist in the subcritical load range but has been proved to exist for only a certain family of reversible systems. Studies have concentrated on symmetric homoclinic solutions and the asymmetric solutions which bifurcate from these solution paths. The primary solution is known to exist for the entire subcritical parameter range and all other symmetric and associated asymmetric solutions exist strictly for values less than critical. Here we uncover a new family of antisymmetric solutions and some asymptotic analysis suggests that the primary antisymmetric solution exists over the same range as does the primary symmetric solution. A perturbation approach can be used to describe the bifurcation hierarchy for the novel antisymmetric forms. We illustrate a unified approach which is able to predict the circumstances under which non-divergent localized solutions are possible and the results of the analysis are compared with some numerical solutions.

Item Details

Item Type:Refereed Article
Keywords:elastic instability, multimodal solutions, exponential asymptotic, boundary-value solutions, strut buckling, solitary wave phenomena
Research Division:Mathematical Sciences
Research Group:Applied mathematics
Research Field:Theoretical and applied mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Bassom, AP (Professor Andrew Bassom)
ID Code:108555
Year Published:1999
Web of Science® Times Cited:21
Deposited By:Mathematics and Physics
Deposited On:2016-04-22
Last Modified:2016-07-08

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