Exact nth derivatives of eigenvalues and eigenvectors

1994 ◽  
Vol 17 (1) ◽  
pp. 136-144 ◽  
Author(s):  
M. S. Jankovic
Keyword(s):  
Eigenvalues And Eigenvectors ◽  
Derivatives Of

Derivatives of Eigenvalues and Eigenvectors of Matrix Functions

1993 ◽  
Vol 14 (4) ◽  
pp. 903-926 ◽  
Author(s):  
Alan L. Andrew ◽  
K.-W. Eric Chu ◽  
Peter Lancaster
Keyword(s):  
Matrix Functions ◽  
Eigenvalues And Eigenvectors ◽  
Derivatives Of

scholarly journals Dynamic and Sensitivity Analysis General Non-Conservative Asymmetric Mechanical Systems

2018 ◽  
Vol 68 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Milan Žmindák
Keyword(s):  
Sensitivity Analysis ◽  
Modal Analysis ◽  
Dynamic Systems ◽  
Mechanical Systems ◽  
Conservative System ◽  
Eigenvalues And Eigenvectors ◽  
Linear Dynamic Systems ◽  
Discretization Methods ◽  
Linear Dynamic ◽  
Derivatives Of

AbstractIn this paper the concept of generalized form of proportional damping is proposed. Classical modal analysis of non-conservative continua is extended to multi DOF linear dynamic systems with asymmetric matrices. Mode orthogonality relationships have been generalized to non-conservative systems. Several discretization methods of continua are presented. Finally, an expression for derivatives of eigenvalues and eigenvectors of non-conservative system is presented. Examples are provided to illustrate the proposed methods.

Direct computation of derivatives of eigenvalues and eigenvectors

1990 ◽  
Vol 36 (3-4) ◽  
pp. 251-255 ◽  
Author(s):  
Alan L Andrew ◽  
Frank R De Hoog ◽  
Roger C.E Tan
Keyword(s):  
Eigenvalues And Eigenvectors ◽  
Direct Computation ◽  
Derivatives Of

Derivatives of eigenvalues and eigenvectors in non-self-adjoint systems.

AIAA Journal ◽  
1973 ◽  
Vol 11 (2) ◽  
pp. 250-251 ◽  
Author(s):  
R. H. PLAUT ◽  
K. HUSEYIN
Keyword(s):  
Eigenvalues And Eigenvectors ◽  
Adjoint Systems ◽  
Derivatives Of

scholarly journals Free-Interface Modal Synthesis Based Substructural Damage Detection Method

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Shanghong Chen ◽  
Wei Lin ◽  
Jiexin Yu ◽  
Ai Qi
Keyword(s):  
Detection Method ◽  
Synthesis Method ◽  
Eigenvalues And Eigenvectors ◽  
Sensitivity Matrix ◽  
Free Interface ◽  
Global Sensitivity ◽  
Modal Synthesis ◽  
Sensitivity Method ◽  
Derivatives Of ◽  
Storey Building

Free-interface modal synthesis method is applied to civil structure, and a substructure method is proposed by introducing the method into global sensitivity method. The substructure expression of the derivatives of eigenvalues and eigenvectors with respect to elemental parameters is obtained. The accuracy of the application of free-interface modal synthesis method is evaluated with different retained modes in substructure, and then the effectiveness of the proposed substructure sensitivity method is illustrated through an 11-storey building under both single- and multidamage cases. Both the damage locations and the extent can be effectively identified. By comparing it with the identical results of global sensitivity method, the proposed method can be faster in detecting the damage location and more stable under multidamage cases. Since this substructure sensitivity method only needs to update sensitivity matrix in the substructure with relative small number of DOFs, it may save much computation effort and become more efficient.

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.

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