On the rotating beam: Some theoretical and numerical results
type: Item
instance of: scholarly article
title: On the rotating beam: Some theoretical and numerical results
zbMATH Open document ID: 0573.73048
DOI: 10.1007/BF02576172
author: B. George
published in: Calcolo
publication date: 1984-01-01T00:00:00Z
review text: The authors study in this clearly written paper the nonlinear plane buckling problem of a beam rotating about its axis, which is clamped at one end and free at the other. By means of Lyapunov Schmidt reduction and singularity theory in the spirit of \textit{M. Golubitsky} and \textit{D. Schaeffer} [e.g. Lect. Notes Pure Appl. Math. 54, 229-254 (1980; Zbl 0438.73044) and Commun. Pure Appl. Math. 32, 21-98 (1979; Zbl 0409.58007)] the complete set of all local solutions of the imperfect problem is given. Finally by means of finite difference methods numerical solutions of the nonlinear boundary value problem are compared with local bifurcation solutions.
Mathematics Subject Classification ID: 74G60
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 3915750
zbMATH Keywords: Golubitsky-Schaeffer theory of singularities
zbMATH Keywords: rotation velocity as bifurcation parameter
zbMATH Keywords: constants describing position of beam are considered as small perturbation parameters
zbMATH Keywords: error analysis
zbMATH Keywords: nonlinear plane buckling
zbMATH Keywords: beam rotating about its axis
zbMATH Keywords: clamped at one end
zbMATH Keywords: free at the other
zbMATH Keywords: Lyapunov Schmidt reduction
zbMATH Keywords: complete set of all local solutions
zbMATH Keywords: imperfect problem
zbMATH Keywords: finite difference methods
zbMATH Keywords: numerical solutions
zbMATH Keywords: nonlinear boundary value problem
zbMATH Keywords: compared with local bifurcation solutions
Wikidata QID: Q57386824
reviewed by: Hans Troger
MaRDI profile type: Publication
cites work: Remarks on the bifurcation of solutions of a nonlinear eigenvalue problem
cites work: Finite dimensional approximation of nonlinear problems. II: Limit points
cites work: A theory for imperfect bifurcation via singularity theory
cites work: A nonlinear eigenvalue problem for rotating rods
description: scientific article; zbMATH DE number 3915750