Localized Vibrations of Disordered Multi-span Beams: Theory and Experiment

The localization of the free modes of vibration of disordered multi-span beams is investigated, both theoretically and experimentally. It is shown that small deviations of the span lengths from an ideal value may have drastic effects on the dynamics of the system, by inhibiting the propagation of vibrations in the structure. Emphasis is placed on the development of a perturbation method that allows one to obtain the localized modes of vibration of the disordered system without a global eigenvalue analysis of the entire system. Such a perturbation analysis is cost effective and accurate. More importantly, it provides physical insight into the localization phenomenon, and allows one to formulate a criterion that predicts the occurence of localized modes. Also, an experiment is described, which has been carried out to verify the existence of localized modes for disordered twospan beams. Theoretical and experimental results are compared in detail and excellent agreement is found, thus confirming the existence of localized modes.