Efficient computation of modal sensitivities for systems with repeated frequencies

The physical origin and ambiguity of repeated frequency modes is discussed, followed by a mathematical derivation of the governing equations for the partial derivatives of repeated eigenvalues with respect to changes in the system parameters. This is followed by a derivation for the associated eigenvector derivative equations. Physical interpretations are included to help explain the analytical results. An efficient computation procedure, which preserves the bandwidth for very large systems, is also proposed for systems with repeated or closely spaced eigenvalues. Two small examples to illustrate the solution procedure are presented. 8 references.