QR-Based Algorithm for Eigenvalue Derivatives

AIAA Journal ◽  
2002 ◽  
Vol 40 (11) ◽  
pp. 2319-2322 ◽  
Author(s):  
Bradley T. Burchett ◽  
Mark Costello
Keyword(s):  
Eigenvalue Derivatives

Modal sensitivities for repeated eigenvalues and eigenvalue derivatives

AIAA Journal ◽  
1992 ◽  
Vol 30 (3) ◽  
pp. 850-852 ◽  
Author(s):  
Jinsiang Shaw ◽  
Suhada Jayasuriya
Keyword(s):  
Repeated Eigenvalues ◽  
Eigenvalue Derivatives

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.

Derivatives of Eigenvalues for Torsional Vibration of Geared Shaft Systems

1993 ◽  
Vol 115 (3) ◽  
pp. 277-279 ◽  
Author(s):  
Liu Zhong-Sheng ◽  
Chen Su-Huan ◽  
Xu Tao
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Design Parameter ◽  
Practical Importance ◽  
Design Sensitivity ◽  
Shaft System ◽  
Eigenvalue Derivatives ◽  
Derivatives Of

Design sensitivity analysis of natural frequency for geared shaft systems is of practical importance in the optimal design of these systems. This note provides a simple and easily implemented method to calculate the eigenvalue derivatives of a geared shaft system with respect to a design parameter ν, including gear inertia J, shaft stiffness K, and transmission ratio Q, when the eigensolution is known. An example is given to illustrate the method.

scholarly journals Higher-order sensitivity analysis of periodic 3-D eigenvalue problems for electromagnetic field calculations

2017 ◽  
Vol 15 ◽  
pp. 215-221 ◽  
Author(s):  
Philipp Jorkowski ◽  
Rolf Schuhmann
Keyword(s):  
Sensitivity Analysis ◽  
Discrete Model ◽  
Eigenvalue Problems ◽  
Periodic Structures ◽  
Higher Order ◽  
Integration Technique ◽  
Periodic Boundaries ◽  
Eigenvalue Derivatives ◽  
Eigenvector Derivatives ◽  
Eigenvalue And Eigenvector

Abstract. An algorithm to perform a higher-order sensitivity analysis for electromagnetic eigenvalue problems is presented. By computing the eigenvalue and eigenvector derivatives, the Brillouin Diagram for periodic structures can be calculated. The discrete model is described using the Finite Integration Technique (FIT) with periodic boundaries, and the sensitivity analysis is performed with respect to the phase shift φ between the periodic boundaries. For validation, a reference solution is calculated by solving multiple eigenvalue problems (EVP). Furthermore, the eigenvalue derivatives are compared to reference values using finite difference (FD) formulas.

QR-based algorithm for eigenvalue derivatives

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 2319-2322
Author(s):  
B. T. Burchett ◽  
M. Costello
Keyword(s):  
Eigenvalue Derivatives

QR based algorithm for eigenvalue derivatives

2001 ◽  
Author(s):  
B.K. Burchett ◽  
Mark Costello
Keyword(s):  
Eigenvalue Derivatives
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