- Pierre, C. and Dowell, E.H., Localization of vibrations by structural irregularity,
J. Sound Vib. (UK), vol. 114 no. 3
pp. 549 - 64 .
(last updated on 2007/04/10)
An investigation of the localization phenomenon is presented for disordered structural systems consisting of weakly coupled component systems. Emphasis is placed on the development of a perturbation method that allows one to obtain the localized modes of vibration of the disordered system from the modes of the individual subsystems. The principal feature of this perturbation method is that it not only considers the variations of the parameters as perturbations, but it also treats the small coupling between subsystems as a perturbation. Such a perturbation analysis is cost effective as compared to a global eigenvalue analysis of the entire system, and proves to be very accurate. Moreover, it provides physical insight into the localization phenomenon, and allows one to formulate a criterion that predicts the occurrence of strongly localized modes. Results are obtained for a chain of single-degree-of-freedom coupled oscillators, but these can be readily generalized to deal with chains of multi-degree-of-freedom component systems