A SINGULAR PERTURBATION ANALYSIS OF EIGENVALUE VEERING AND MODAL SENSITIVITY IN PERTURBED LINEAR PERIODIC-SYSTEMS

An investigation into the eigenvalue loci veering and modal sensitivity is presented for mistuned structural systems. Examples from both the weakly coupled uniaxial component systems and the cyclic symmetric systems are considered. The analysis is based on singular perturbation techniques. It is shown that uniform asymptotic expansions for the eigenvalues and eigenvectors can be constructed in terms of the mistuning parameters, and that these solutions are in excellent agreement with the exact solutions. The modal sensitivity function and the eigenvector rotations are then used to show the singular behavior of the eigenvectors in the neighborhood of a singular point. Rapid changes in the sensitivity function may signify large relative differences in the amplitudes of forced vibratory response between the tuned and the mistuned states. © 1993 Academic Press Limited.