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 direct algebraic method for eigensolution sensitivity computation of damped asymmetric systems
TL;DR: In this article, a new approach is presented for calculating simultaneously the derivatives of the eigenvector of a vibrating symmetric system for which the left and right eigenvectors and their derivatives become distinct and complex.
Proceedings ArticleDOI
Multivariable isoperformance methodology for precision opto-mechanical systems
de Weck,Olivier Ladislas +1 more
TL;DR: Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2001 as discussed by the authors, was the first work to address the problem of space flight.
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Damage Identification in a Truss Tower by Regularized Model Updating
TL;DR: In this article, the authors presented a sensitivity-based damage identification of a three-dimensional truss tower tested in the laboratory, where a finite-element model is updated by modal parameters obtained from ambient vibration measurements.
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Reliability analysis of a satellite structure with a parametric and a non-parametric probabilistic model
Manuel F. Pellissetti,Evangéline Capiez-Lernout,Helmut J. Pradlwarter,Christian Soize,Gerhart I. Schuëller +4 more
TL;DR: In this paper, the reliability of a satellite structure subjected to harmonic base excitation in the low frequency range is analyzed with respect to the exceedance of critical frequency response thresholds, where both a parametric model of uncertainties and a more recently introduced non-parametric model are used to analyze the reliability.
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.