Vibration analysis of quasi-symmetric structures
type: Item
instance of: scholarly article
title: Vibration analysis of quasi-symmetric structures
zbMATH Open document ID: 0626.73067
DOI: 10.1016/0168-874X(87)90009-6
author: Ahmed K. Noor
author: Sandra L. Whitworth
published in: Finite Elements in Analysis and Design
publication date: 1987-01-01T00:00:00Z
review text: An efficient computational procedure is presented for the free vibration analysis of structures with unsymmetric geometry. The procedure is based on approximating the unsymmetric vibrational response of the structure by a linear combination of a few symmetric and antisymmetric modes (global approximation vectors), each obtained using approximately half the degrees of freedom of the original model. The three key elements of the procedure are: (a) use of mixed finite element models having independent shape functions for the internal forces (stress resultants) and generalized displacements, with the internal forces allowed to be discontinuous at interelement boundaries, (b) operator splitting, or additive decomposition of the different arrays in the governing finite element equations to delineate the contributions to the symmetric and antisymmetric response vectors, and (c) use of a reduction method through successive application of the finite element method and the classical Bubnov-Galerkin technique. The finite element method is first used to generate a few symmetric and antisymmetric global approximation response vectors. Then, the classical Bubnov-Galerkin technique is used to substantially reduce the size of the eigenvalue problem. An initial set of global approximation vectors is selected to be a few symmetric and antisymmetric eigenvectors and their various-order derivatives with respect to a tracing parameter identifying all the correction terms to the symmetric (and antisymmetric) eigenvectors. A modified (improved) set of approximation vectors is obtained by using the inverse iteration procedure. The effectiveness of the proposed procedure is demonstrated by means of a numerical example.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 4018518
zbMATH Keywords: free vibration
zbMATH Keywords: unsymmetric geometry
zbMATH Keywords: approximating the unsymmetric vibrational response
zbMATH Keywords: linear combination of a few symmetric and antisymmetric modes
zbMATH Keywords: global approximation vectors
zbMATH Keywords: mixed finite element models
zbMATH Keywords: operator splitting
zbMATH Keywords: reduction method
zbMATH Keywords: Bubnov-Galerkin technique
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: inverse iteration procedure
MaRDI profile type: Publication
full work available at URL: 0168-874x(87)90009-6
OpenAlex ID: W4232030077
description: scientific article; zbMATH DE number 4018518