Some simple mechanical systems with a post-buckling path bifurcating at infinity
type: Item
instance of: scholarly article
title: Some simple mechanical systems with a post-buckling path bifurcating at infinity
zbMATH Open document ID: 0581.73057
DOI: 10.1007/BF01177056
published in: Acta Mechanica
publication date: 1986-01-01T00:00:00Z
review text: It is shown, that simple structures composed of rigid bodies exist, which possess an equilibrium position, that is stable for all finite loadings, and a post-buckling path bifurcating off for the loading at infinity. This property only occurs for the perfect system as imperfect systems have a finite critical loading. Methods of singularity theory are applied to investigate this type of bifurcation. In simple cases it is possible to give the full (versal) unfolding by means of catastrophe theory. But for higher dimensional cases especially adapted concepts are considered to be the proper mean, particularly as common reduction principles do not work for this type of bifurcation. To show that bifurcation at infinity does not only occur for static problems a reference to an example from hydrodynamics is given.
Mathematics Subject Classification ID: 74G60
zbMATH DE Number: 3930470
zbMATH Keywords: two mechanical examples
zbMATH Keywords: extreme imperfection sensitivity
zbMATH Keywords: weakened form of generic bifurcation
zbMATH Keywords: Hale's concept
zbMATH Keywords: robustness of transversality
zbMATH Keywords: simple structures composed of rigid bodies
zbMATH Keywords: equilibrium position
zbMATH Keywords: stable for all finite loadings
zbMATH Keywords: post-buckling path bifurcating off for the loading at infinity
zbMATH Keywords: perfect system
zbMATH Keywords: singularity theory
zbMATH Keywords: full (versal) unfolding
zbMATH Keywords: catastrophe theory
author: Rudolf Scheidl
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3930470