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
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Proceedings ArticleDOI
Optimization of Aircraft Wings Including Dynamic Aeroelasticity and Manufacturing Aspects
TL;DR: An efficient semi-analytical method for the determination of the gust load response sensitivities to structural sizing variables that has been implemented within an industrial structural optimization package and its application to a simple example is described.
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FEM Sensitivity Method for Uncertainty and Reconciliation Analyses
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Improved modal truncation method for eigensensitivity analysis of asymmetric matrix with repeated eigenvalues
TL;DR: In this article, an improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second and third-order eigenvalue derivatives and the first-and second-order Eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues.
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Kron's substructuring method to the calculation of structural responses and response sensitivities of nonlinear systems
Wei Tian,Shun Weng,Yong Xia +2 more
TL;DR: In this article, the structural responses and response sensitivities are calculated from the reduced vibration equation of a relatively large-scale nonlinear frame and the precision and efficiency of the proposed method are verified by a nonlinear spring-mass system and a relatively small-scale structural frame.
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Topology optimization with superelements
Ren-Jye Yang,C. M. Lu +1 more
TL;DR: In this article, the target panel was modeled as the residual structure and the rest as one big substructure, and only one optimization loop was required and no analysis approximation was made during optimization iterations.
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.