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.

On Derivatives and Norms of Generalized Matrix Functions and Respective Symmetric Powers

2015 ◽  
Vol 30 ◽  
Author(s):  
Sonia Carvalho ◽  
Pedro Freitas
Keyword(s):  
Symmetric Group ◽  
Symmetric Tensor ◽  
Directional Derivatives ◽  
Matrix Functions ◽  
Tensor Power ◽  
Symmetric Powers ◽  
Generalized Matrix ◽  
Derivatives Of

In recent papers, S. Carvalho and P. J. Freitas obtained formulas for directional derivatives, of all orders, of the immanant and of the m-th $\xi$-symmetric tensor power of an operator and a matrix, when $\xi$ is a character of the full symmetric group. The operator bound norm of these derivatives was also calculated. In this paper similar results are established for generalized matrix functions and for every symmetric tensor power.

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.

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