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
Eigenvector sensitivity when tracking modes with repeated eigenvalues
TL;DR: This paper proposes a general framework for computing eigenvector sensitivity whenever tracking specific mode shapes selected beforehand, with emphasis on the multiple eigenvalues case.
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Anisotropic damage model for an inclined crack in thick plate and sensitivity study for its detection
D. Wu,Siu-Seong Law +1 more
TL;DR: In this paper, an anisotropic damage model is proposed for a thick plate element with an inclined crack, where the cracked plate element is represented by an effective plate element and a vector of damage variables.
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Vibration analysis of laminated anisotropic shells of revolution
A. K. Noor,J. M. Peters +1 more
TL;DR: In this paper, an analytical formulation is presented for free vibration analysis of laminated anisotropic shells of revolution, and for assessing the sensitivity of their response to nonorthotropic (non-orthotropic) material coefficients.
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Accelerated subspace iteration for eigenvector derivatives
TL;DR: In this paper, an accelerated subspace iteration method for calculating eigenvector derivatives has been developed, and effective strategies concerning the effectiveness and reliability of the subspace iterations are presented.
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Eigensolutions sensitivity analysis using a sub-structuring method
TL;DR: In this paper, the modal synthesis computation tool offers the flexibility required so as to anticipate the vibratory behavior of the complex structure in the design process, and it is easy to take into account the successive modification involved in various elements optimization.
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.