Journal ArticleDOI
Simplified calculation of eigenvector derivatives
Reads0
Chats0
TLDR
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
More filters
Journal ArticleDOI
Results obtained by minimising natural frequency and mac-value errors of a plate model
K. Bohle,Claus-Peter Fritzen +1 more
TL;DR: In this paper, a plate model of the Garteur structure has been developed and updated and the cost function for the evaluation of the model's improvement consisted of residuals between calculated and measured natural frequencies and mode shapes.
Journal ArticleDOI
Higher order eigensensitivity analysis of damped systems with repeated eigenvalues
TL;DR: In this article, a simplified method for the computation of first-, second-and higher-order derivatives of eigenvalues and eigenvectors associated with repeated eigen values is presented.
Identification of Non-linear Joint Parameters by using Frequency Response Residuals
TL;DR: In this article, the harmonic balance method is used for the calculation of effective stiffness and damping coefficients of non-linear joints between linear substructures to characterize the properties of the nonlinear joints.
Journal ArticleDOI
Second-order eigensensitivity analysis of asymmetric damped systems using Nelson's method
TL;DR: In this paper, the second-order derivatives of the eigenvalues and eigenvectors of symmetric and asymmetric damped systems were derived using the first-order eigensensitivity analysis using Nelson's method.
Journal ArticleDOI
A study on design sensitivity analysis for general nonlinear eigenproblems
Li Li,Yujin Hu,Xuelin Wang +2 more
TL;DR: In this article, the design sensitivity analysis for the general nonlinear eigenproblem with respect to arbitrary design parameters is studied, and the derivatives of eigensolutions can be treated in a unified way for different structural systems (i.e., undamped systems, viscously and nonviscously damped systems and nonlinear systems).
References
More filters
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.