Abstract
Derivatives of eigenvectors with respect to structural parameters play an important role in structural design, identification, and optimization. Particularly, calculation of eigenvector sensitivity is considered when the eigenvalues are repeated. A relaxation factor embedded in the combined approximations (CA) method makes it effective to the structural response at various modified designs. The proposed method is feasible after overcoming the defection of irreversibility of the characteristic matrix. Numerical examples show that it is easy to implement the computational procedure, and the method presented in this paper is efficient for the general linear vibration damped systems with repeated frequencies.
Highlights
Many engineering optimization problems, for example, model updating [1] or structural damage detections [2], lead to a sensitivity analysis of eigenproblems
A relaxation factor embedded in the combined approximations (CA) method is to keep the reversibility of the characteristic matrix which makes it possible and effective to deal with the problems of sensitivity analysis for multiple eigenvalues
The extension of CA method is outlined to enable the calculation of eigenvectors sensitivity analysis for general linear damped vibration systems with repeated eigenvalues
Summary
For example, model updating [1] or structural damage detections [2], lead to a sensitivity analysis of eigenproblems. A dynamic model can be far from the assumed prototype because there is usually a variation, such as a mistuned parameter or a geometrical irregularity For these reasons, sensitivity analysis is meaningful to perform a theoretical study and give a guide for engineering practice. Nelson [6] proposed a very efficient algorithm for eigenvector derivatives that only requires those eigensolutions information which is to be differentiated This method cannot deal with cases of repeated eigenvalues which can often occur in many practical engineering problems. In choosing a suitable sensitivity analysis method for the system with repeated eigenvalues, the following two factors should be well balanced: the accuracy of the calculations and Journal of Applied Mathematics the computational effort involved.
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