Eigenvalue and eigenvector computation for discrete and continuous structures composed of viscoelastic materials

Both discrete and continuous structures, with frequency and/or temperature dependent viscoelastic elements, gives rise to a nonlinear eigenvalue problem. An accurate computation of eigenvalues (natural frequencies) and eigenvectors (mode shapes) is essential for control, design sensitivities, and op...

Full description

Saved in:
Bibliographic Details
Published in:International journal of mechanical sciences Vol. 110; pp. 127 - 137
Main Author: Singh, Kumar Vikram
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.05.2016
Subjects:
Approximation
Computation
Discrete and continuous systems
Eigenvalues
Eigenvectors
Left and right eigenvectors
Mathematical analysis
Mathematical models
Nonlinear eigenvalue problems
Nonlinearity
Numerical method
Sensitivity
Viscoelastic material
Viscoelasticity
Left and right eigenvectors
Sensitivity
Numerical method
Viscoelastic material
Nonlinear eigenvalue problems
Discrete and continuous systems
ISSN:0020-7403, 1879-2162
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Both discrete and continuous structures, with frequency and/or temperature dependent viscoelastic elements, gives rise to a nonlinear eigenvalue problem. An accurate computation of eigenvalues (natural frequencies) and eigenvectors (mode shapes) is essential for control, design sensitivities, and optimization studies. In this paper, a pth order approximation of a general nonlinear eigenvalue problem is formulated. A numerical approach to simultaneously compute the eigenvalues and associated left and right eigenvectors is presented. This method can be used for both discrete and continuous systems with viscoelastic elements. Numerical examples are presented here to demonstrate its effectiveness and for the validation purposes. •Eigenvalues and eigenvectors computation for viscoelastic system is presented.•A higher order iteration method for solving associated nonlinear eigenvalue problem is developed.•Computational efficiency and selection basis for approximation order is presented.•Proposed approach does not require computation of determinants and their derivatives.•Estimated eigenvalues, complex modes shapes and design sensitivities are validated against analytical methods.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0020-7403
1879-2162
DOI:10.1016/j.ijmecsci.2016.03.009