Computerized symbolic solution for a nonconservative system in which instability occurs by flutter in one range of a parameter and by divergence in another
type: Item
instance of: scholarly article
title: Computerized symbolic solution for a nonconservative system in which instability occurs by flutter in one range of a parameter and by divergence in another
zbMATH Open document ID: 0607.73051
DOI: 10.1016/0045-7825(87)90088-0
author: Isaac Elishakoff
author: Joseph Hollkamp
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1987-01-01T00:00:00Z
review text: The instability of a uniform column which is simply supported at one end, resting on a support at some intermediate location q, and has the other end subjected to a follower force is studied. The problem is solved by the Galerkin method in conjunction with computerized symbolic algebra. It is shown that there exists a location for the intermediate support at \(q=q^*\) so that the structure loses its stability by flutter for \(q<q^*\), and by divergence for \(q>q^*\). At \(q=q^*\) the critical load undergoes a jump, implying the transition of the instability mode from flutter to divergence. Moreover, the location \(q=q^*_+\) is an optimal location in the sense that the critical load assumes a maximum.
Mathematics Subject Classification ID: 74G60
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 70J30
zbMATH DE Number: 3982655
zbMATH Keywords: instability
zbMATH Keywords: uniform column
zbMATH Keywords: simply supported at one end
zbMATH Keywords: resting on a support at some intermediate location
zbMATH Keywords: other end subjected to a follower force
zbMATH Keywords: Galerkin method
zbMATH Keywords: computerized symbolic algebra
zbMATH Keywords: critical load
zbMATH Keywords: jump
zbMATH Keywords: transition of the instability mode from flutter to divergence
describes a project that uses: REDUCE
MaRDI profile type: Publication
full work available at URL: 0045-7825(87)90088-0
OpenAlex ID: W2090926765
cites work: Die Knicklast des einseitig gespannten, tangential gedrückten Stabes
cites work: Q4042721
cites work: Application of the Galerkin and Ritz methods to nonconservative problems of elastic stability
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description: scientific article; zbMATH DE number 3982655