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Derivatives of eigenvectors with respect to structural parameters play an important role in structural design,identification,and optimization.This paper considers the calculation of eigenvector sensitivity when the eigenvalues are repeated.A relaxation factor embedded in the combined approximations method makes it effective to the structural response at various modified designs.The proposed method is feasible after overcoming the difficulties of irreversible condition.The numerical example shows that it is easy and efficient to implement this method for the general linear vibration damped systems with repeated frequencies.