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A direct algebraic method for eigensolution sensitivity computation of damped asymmetric systems
Author(s) -
Guedria Najeh,
Smaoui Hichem,
Chouchane Mnaouar
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1732
Subject(s) - eigenvalues and eigenvectors , singularity , mathematics , computation , modal , algebraic number , algebraic equation , mathematical analysis , nonlinear system , physics , algorithm , chemistry , quantum mechanics , polymer chemistry
In general, the derivative of an eigenvector of a vibrating symmetric system is the solution of a singular problem. Further complications are encountered in dealing with asymmetric damped systems for which the left and right eigenvectors and their derivatives become distinct and complex. Several approaches have been proposed to overcome this singularity such as Nelson's method and the modal method. In the present work, a new approach is presented for calculating simultaneously the derivatives of the eigenvalues and their associated derivatives of the left and right eigenvectors for asymmetric damped systems. With the proposed method, the exact eigenderivatives can be obtained by solving a first‐order linear algebraic system of equations. The method is applied on a 104 DOF ventilator–rotor system, which is used as an example of an asymmetric damped system with distinct eigenvalues. The diameter of the shaft has been chosen as the design parameter. The comparison of the computational time shows that the proposed method is more efficient than both Nelson's approach and the modal method. Copyright © 2006 John Wiley & Sons, Ltd.