An efficient method for computing eigenpair sensitivity of asymmetric damped systems with repeated eigenvalues

This paper presents a new algorithm for computing the sensitivity of eigenpairs in asymmetric damped systems with repeated eigenvalues. The derivatives of eigenvectors in such systems are divided into particular and homogeneous solutions. An effective strategy for constructing non-singular coefficient matrices is proposed to calculate the particular solutions. The present method only needs to consider the modal information of repeated frequencies for calculating eigenpair sensitivity, it does not need to expand the order of the system and rearrange the matrices. Hence, we can minimize the “fill-in” operation to the sparse matrices of the system, this facilitates the integration of this algorithm into existing commercial software packages. Two rotor dynamic systems are considered in this work to demonstrate the effectiveness of the proposed algorithm.