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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 Modal Derivative Enhanced Kron’s Substructuring Method for Response and Response Sensitivities of Geometrically Nonlinear Systems
TL;DR: In this paper , a substructuring method was developed to calculate responses and sensitivities of structures with geometric nonlinearities using modal derivatives, which can be used to calculate structural responses, response sensitivities, and model updating.
Derivatives of eigenpairs of symmetric quadratic eigenvalue problem
Xie Huiqing,Dai Hua +1 more
TL;DR: The derivatives are calculated in terms of the eigenvalues and eigenvectors of the quadratic eigenvalue problem, and the use of state space repre- sentation is avoided, hence the cost of computation is greatly reduced.
Journal ArticleDOI
Investigation of a Software for Finite Element Model Updating of Bridges Based on Interface Technology between VC++ and MATLAB
Yang Liu,Zhan Lv,Hong Zhang +2 more
TL;DR: To develop an effective software for finite element (FE) model updating of bridges, the interface technology between VC++ and MATLAB was investigated firstly, and then a software, named Doctor for Bridges (version 1.0) was developed.
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.