Journal ArticleDOI
Simplified calculation of eigenvector derivatives
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A simplified procedure is presented for the determination of the derivatives of eigenvectors of nth order algebraic eigensystems, applicable to symmetric or nonsymmetric systems, and requires knowledge of only one eigenvalue and its associated right and left eigenavectors.Abstract:
A simplified procedure is presented for the determination of the derivatives of eigenvectors of nth order algebraic eigensystems. The method is applicable to symmetric or nonsymmetric systems, and requires knowledge of only one eigenvalue and its associated right and left eigenvectors. In the procedure, the matrix of the original eigensystem of rank (/?-!) is modified to convert it to a matrix of rank /?, which then is solved directly for a vector which, together with the eigenvector, gives the eigenvector derivative to within an arbitrary constant. The norm of the eigenvector is used to determine this constant and complete the calculation. The method is simple, since the modified n rank matrix is formed without matrix multiplication or extensive manipulation. Since the matrix has the same bandedness as the original eigensystems, it can be treated efficiently using the same banded equation solution algorithms that are used to find the eigenvectors.read more
Citations
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Journal ArticleDOI
A review on dynamic substructuring methods for model updating and damage detection of large-scale structures:
TL;DR: This article reviews widely used dynamic substructuring methods for model updating and damage identification of large-scale structures and assembles the vibration properties of each substructure into those of the substructures.
Journal ArticleDOI
Stability analysis of thermo-acoustic nonlinear eigenproblems in annular combustors. Part I. Sensitivity
TL;DR: By solving only one adjoint eigenproblem, the sensitivities to any thermo-acoustic parameter are obtained, which match the finite-difference solutions at much lower computational cost.
Book ChapterDOI
Finite Element Modelling
M. I. Friswell,J. E. Mottershead +1 more
TL;DR: The finite element method has become established as the universally accepted analysis method in structural design as discussed by the authors, which leads to the construction of a discrete system of matrix equations to represent the mass and stiffness effects of a continuous structure.
Journal ArticleDOI
Higher order sensitivities in structural systems
TL;DR: In this paper, the free energy contribution of the acoustic degrees of freedom of high-temperature gases was investigated under nonequilibrium conditions, particularly if the acoustic fluctuations exhibit intensity levels corresponding to turbulence.
Journal ArticleDOI
New mode tracking methods in aeroelastic analysis
TL;DR: In this article, a methodology for the tracking of complex eigenvalues and eigenvectors through changes in aeroelastic eigenvalue problems is developed for the analysis of finite element models.
References
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Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Journal ArticleDOI
Rates of change of eigenvalues and eigenvectors.
R. L. Fox,M. P. Kapoor +1 more
TL;DR: Exact expressions for rates of change of eigenvalues and eigenvector to facilitate computerized design of complex structures are presented.
Journal ArticleDOI
Statistical Identification of Structures
TL;DR: In this paper, a method is formulated for systematically using experimental measurements of the natural frequencies and mode shapes of a structure to modify stiffness and mass characteristics of a finite element model, and an additional feature is that the engineer's confidence in the modeling of the various finite elements is quantified and incorporated into the revision procedure.
Journal ArticleDOI
Handbook for Automatic Computation. Vol II, Linear Algebra
James Hardy Wilkinson,C. Reinsch +1 more
TL;DR: Haida gwaii tourism guide, Handbook of raman spectroscopy, and the Jordan form, Kronecker's form for matrix pencils, and various condition in the Handbook.