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.
"Efficient Procedures of Sensitivity Analysis for Structural Vibration Systems with Repeated Frequencies." J. Appl. Math. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/810147