An investigation into the eigenvalue loci veering and mode localization phenomenon 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 these solutions are in excellent agreement with the exact solutions. The asymptotic expansions are then used to clearly show how the singular behavior in the eigenfunctions or modeshapes leads to mode localization.

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