Sensitivity Analysis of the Eigenvector in the Non-Conservative System with Repeated Eigenvalues

A modal method for computing sensitivities of the eigenvectors of a non-conservative system with repeated eigenvalues by using matrix analysis in the presence of a first-order system is proposed. The characteristic matrixes of system are not limited by the restrictions of symmetric and positive definiteness. And it successfully avoids the effects of multiple eigenvalues. The simplicity and economy have been now established during the reasoning and implementing processes. A numerical example is presented to demonstrate the efficiency and correctness of the modal method proposed.