Free vibration analysis of rotating nonlinearly elastic structures with symmetry: An efficient group-equivariance approach
type: Item
instance of: scholarly article
title: Free vibration analysis of rotating nonlinearly elastic structures with symmetry: An efficient group-equivariance approach
zbMATH Open document ID: 0879.73035
DOI: 10.1023/A:1008214713699
author: Timothy M. Whalen
author: Timothy J. Healey
published in: Nonlinear Dynamics
publication date: 1997-09-09T00:00:00Z
review text: We show that the use of group-theoretic ideas can greatly simplify the procedure for finding both linear vibration modes and frequencies and locating solution branches for nonlinear vibration problems. These methods can be employed in both analytic and numerical settings, and they lead to dramatic increases in solving efficiency via block diagonalization. For the class of problems studied here (in which gyroscopic effects are present), we demonstrate that the original structural symmetry group can be employed to analyze the dynamics of the system despite the loss of reflection symmetry. In addition, we explain how ideas from bifurcation theory can be included with symmetry analysis to prove the existence of solution branches for nonlinear vibration problems.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 1042661
zbMATH Keywords: block diagonalization
zbMATH Keywords: gyroscopic effects
zbMATH Keywords: bifurcation theory
zbMATH Keywords: existence of solution branches
MaRDI profile type: Publication
full work available at URL: a:1008214713699
OpenAlex ID: W325780213
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description: scientific article; zbMATH DE number 1042661