Analysis of the vibration localization phenomenon in imperfect rings

The modal analysis of imperfect rings vibrating in their own plane is considered in this paper. The imperfections are modeled as generic perturbations, depending on the angular variable, of the linear mass density and the bending stiffness of the ring. The Euler-Bernoulli theory is used to develop the dynamical model of the ring, and a perturbation expansion of the solution is performed in order to find out the modal split eigenfrequencies and the relevant perturbed modal shapes. Finally, some case-study problems are considered and the analytical results obtained by using the proposed approach are compared to results obtained by employing a finite-element model of the imperfect ring.