Detection of damage in cyclic structures using an eigenpair sensitivity matrix

In cyclic structures, the eigenvectors associated with repeated eigenvalues do not change smoothly in case of damages, thus, the existing sensitivity-based damage detection techniques are rendered ineffective. To overcome this problem, a transformation from such eigenvectors to a set of well-behaved pseudo-eigenvectors is introduced. The proposed pseudo-eigenvectors can be linearly approximated, and hence, they admit sensitivity-based analysis. Subsequently, sensitivity matrices of eigenvalues and pseudo-eigenvectors are established, and four damage detection algorithms are developed accordingly. Simulation results under different number of sensors and various noise levels confirm the efficiency of the proposed approach.