An Exact Method for Calculating the Eigenvector Sensitivities

Abstract

Eigenvector sensitivities are often used in many engineering problems such as structural vibration control, optimization design, model updating and damage identification. So far, modal superposition method and Nelson’s method are the two main methods for exactly calculating eigenvector sensitivities. However, modal superposition method has a great limitation in applications because it needs all the eigenvectors in its calculation. Although Nelson’s method does not need to use all the eigenvectors, there is no unified sensitivity calculation formula for each eigenvector. In this paper, a new exact method for calculating the eigenvector sensitivity is proposed. The explicit expressions for the first-order and second-order sensitivities of eigenvectors are derived, and strict proof is given. The developed eigenvector sensitivity formulas are simple and convenient in programming. The proposed method is as powerful as Nelson’s method, but much more easy to use. Two numerical examples are used to demonstrate the proposed method and the results show that the developed eigenvector sensitivity formulas are exact and reliable.