A multiplicative eigenvalues perturbation and its application to natural frequency assignment in undamped second-order systems

In this article, a novel theorem for eigenvalue perturbation inspired by the results of Brauer is introduced. The new result is valid for single and multiple eigenvalue perturbations, with preservation—no spillover of the remaining spectrum. An application of the proposed results is given since the model updating and the partial eigenvalue assignment problems for second-order linear dynamics have gained crescent attention in the last decades. Furthermore, its effectiveness is illustrated with numerical examples.