Eigenvector Derivatives of Generalized Nondefective Eigenproblems With Repeated Eigenvalues

1995 ◽  
Vol 117 (1) ◽  
pp. 207-212 ◽  
Author(s):  
Y.-Q. Zhang ◽  
W.-L. Wang
Keyword(s):  
Recent Work ◽  
New Method ◽  
First Eigenvalue ◽  
Numerical Examples ◽  
Repeated Eigenvalues ◽  
Generalized Eigenproblem ◽  
Eigenvalue Derivatives ◽  
Eigenvector Derivatives ◽  
Eigenvalue And Eigenvector ◽  
Derivatives Of

A new method is presented for computation of eigenvalue and eigenvector derivatives associated with repeated eigenvalues of the generalized nondefective eigenproblem. This approach is an extension of recent work by Daily and by Juang et al. and is applicable to symmetric or nonsymmetric systems. The extended phases read as follows. The differentiable eigenvectors and their derivatives associated with repeated eigenvalues are determined for a generalized eigenproblem, requiring the knowledge of only those eigenvectors to be differentiated. Moreover, formulations for computing eigenvector derivatives have been presented covering the case where multigroups of repeated first eigenvalue derivatives occur. Numerical examples are given to demonstrate the effectiveness of the proposed method.

Eigenvector Derivatives of Generalized Nondefective Eigenproblems With Repeated Eigenvalues

1993 ◽  
Author(s):  
Yong-Qiang Zhang ◽  
Wen-Liang Wang
Keyword(s):  
Recent Work ◽  
New Method ◽  
First Eigenvalue ◽  
Numerical Examples ◽  
Repeated Eigenvalues ◽  
Generalized Eigenproblem ◽  
Eigenvalue Derivatives ◽  
Eigenvector Derivatives ◽  
Eigenvalue And Eigenvector ◽  
Derivatives Of

A new method is presented for computation of eigenvalue and eigenvector derivatives associated with repeated eigenvalues of the generalized nondefective eigenproblem. This approach is an extension of recent work by Dailey and by Juang et al. and is applicable to symmetric or nonsymmetric systems. The extended phases read as follows. The differentiable eigenvectors and their derivatives associated with repeated eigenvalues are determined for generalized eigenproblem, requiring the knowledge of only those eigenvectors to be differentiated. Moreover, formulations for computing eigenvector derivatives have been presented covering the case where multi-groups of repeated first eigenvalue derivatives occur. Numerical Examples are given to demonstrate the effectiveness of the proposed method.

The Derivatives of Repeated Eigenvalues and Their Associated Eigenvectors

1996 ◽  
Vol 118 (3) ◽  
pp. 390-397 ◽  
Author(s):  
M. I. Friswell
Keyword(s):  
Taylor Series ◽  
Design Parameters ◽  
Eigenvalues And Eigenvectors ◽  
First Order ◽  
Repeated Eigenvalues ◽  
Eigenvector Derivatives ◽  
Eigenvalue And Eigenvector ◽  
Derivatives Of

This paper considers the calculation of eigenvalue and eigenvector derivatives when the eigenvalues are repeated. An extension to Nelson’s method is used to calculate the first order derivatives of eigenvectors when the derivatives of the associated eigenvalues are also equal. The continuity of the eigenvalues and eigenvectors is discussed, and the discontinuities in the eigenvectors, when they are regarded as functions of two or more design parameters, is demonstrated. The validity of Taylor series for the eigenvalues and eigenvectors is examined and the use of these series critically assessed.

Eigenvalue and eigenvector derivatives of a nondefective matrix

1989 ◽  
Vol 12 (4) ◽  
pp. 480-486 ◽  
Author(s):  
Jer-Nan Juang ◽  
Peiman Ghaemmaghami ◽  
Kyong Been Lim
Keyword(s):  
Eigenvector Derivatives ◽  
Eigenvalue And Eigenvector ◽  
Derivatives Of

Computation of Eigenvalues and Eigenvectors of a Mistuned Bladed Disk

2006 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Eigenvalues And Eigenvectors ◽  
Numerical Examples ◽  
Bladed Disk ◽  
Repeated Eigenvalues ◽  
Derivatives Of ◽  
Computation Of Eigenvalues

This paper deals with fundamental aspects of variations in eigenvalues and eigenvectors of a bladed disk due to mistuning. First, the existence of derivatives of repeated eigenvalues and corresponding eigenvectors is thoroughly examined. Next, an algorithm is developed to compute these derivatives. It is shown how a Taylor series expansion can be used to efficiently compute eigenvalues and eigenvectors of a mistuned system. This methodology is developed for perturbations in both repeated and unrepeated eigenvalues of the tuned system. Lastly, numerical examples are presented.

Computation of Eigenvalues and Eigenvectors of a Mistuned Bladed Disk Via Unidirectional Taylor Series Expansions

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Taylor Series ◽  
Taylor Series Expansion ◽  
Series Expansions ◽  
Eigenvalues And Eigenvectors ◽  
Numerical Examples ◽  
Bladed Disk ◽  
Repeated Eigenvalues ◽  
Taylor Series Expansions ◽  
Derivatives Of ◽  
Computation Of Eigenvalues

This paper deals with the computation of eigenvalues and eigenvectors of a mistuned bladed disk. First, the existence of derivatives of repeated eigenvalues and corresponding eigenvectors is discussed. Next, an algorithm is developed to compute these derivatives. It is shown how a Taylor series expansion can be used to efficiently compute eigenvalues and eigenvectors of a mistuned system. Numerical examples are presented to corroborate the validity of theoretical analysis.

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