scholarly journals Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials

2018 ◽  
Vol 88 (315) ◽  
pp. 313-347 ◽  
Author(s):  
Jared Aurentz ◽  
Thomas Mach ◽  
Leonardo Robol ◽  
Raf Vandebril ◽  
David S. Watkins
Keyword(s):  
Eigenvalues And Eigenvectors ◽  
Matrix Polynomials ◽  
Stable Computation ◽  
Computation Of Eigenvalues

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.

scholarly journals Application of the Perturbation Method for Determination of Eigenvalues and Eigenvectors for the Assumed Static Strain

2014 ◽  
Vol 10 (2) ◽  
pp. 111-120
Author(s):  
Izabela Major ◽  
Maciej Major
Keyword(s):  
Perturbation Method ◽  
Wave Amplitude ◽  
Homogeneous State ◽  
Eigenvalues And Eigenvectors ◽  
Static Strain ◽  
Non Linear ◽  
Computation Of Eigenvalues ◽  
Unit Vectors

Abstract The paper presents the perturbation method which was used for computation of eigenvalues and eigenvectors for the assumed homogeneous state of strain in the hyperelastic Murnaghan material. The values calculated might be used for determination of the rate of propagation of unit vectors of wave amplitude for other non-linear

Modelling of Vibratory Bowl Feeders

1986 ◽  
Vol 200 (6) ◽  
pp. 431-437 ◽  
Author(s):  
D Morrey ◽  
J E Mottershead
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Rigid Base ◽  
Eigenvalues And Eigenvectors ◽  
Leaf Springs ◽  
Lumped Parameter ◽  
Matrix Manipulation ◽  
Bowl Feeder ◽  
Parameter Approach ◽  
Computation Of Eigenvalues

The modelling of vibratory bowl feed systems can be considered in two parts, namely the simulation of (a) the bowl feeder structure vibrations and (b) the behaviour of the components under feed conditions. This paper deals with the former problem using a lumped parameter approach, whereby a rigid bowl and rigid base are separated by three banks of flexible leaf springs. Natural frequencies and mode shapes computed from the model are compared with those obtained by experimental modal analysis of a parts feeder. The model can be easily implemented on a digital computer using standard NAG routines for matrix manipulation and computation of eigenvalues and eigenvectors.

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