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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A framework for computer vision-based health monitoring of a truss structure subjected to unknown excitations
Mariusz Ostrowski,Bartlomiej Blachowski,Bartosz Wójcik,Mateusz Żarski,Piotr Tauzowski,Łukasz Jankowski +5 more
Proceedings ArticleDOI
A generalized influence measure for fuzzy uncertainty analysis
Nico-Philipp Walz,Michael Hanss +1 more
TL;DR: This contribution presents a generalized formulation of the influence measures of fuzzy arithmetic so that they are applicable for uncertainty analysis in a universal sense where the uncertainties are described by fuzzy numbers or intervals.
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Substructuring Method for Eigensensitivity
TL;DR: In this paper , the eigensensitivity equation is derived based on the reduced eigenequation of the substructuring method developed in Chap. 2 , where only the derivatives of the master modes of one substructure are calculated, and derivatives of discarded slave modes are compensated by the derivative of residual flexibility.
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Dynamic Condensation Approach to Finite Element Model Updating
TL;DR: In this paper , the IOR method was extended to the sensitivity-based FE model updating using modal data (eigensolutions) and time history data (structural responses).
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Improved Structural Health Monitoring Using Mode Shapes: An Enhanced Framework for Damage Detection in 2D and 3D Structures
TL;DR: In this paper , a modified version of Wang's method was proposed to produce a sensitivity equation for the damaged structures by considering reducing the stiffness of elements in the damage scenarios, including both two-dimensional and three-dimensional structures.
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.