Numerical study of vibration localization in disordered cyclic structures

A study of mode localization in disordered cyclic structures that have multi-degree-of-freedom substructures in presented. Particular emphasis is placed on the transition of the natural modes from being extended throughout the structure to being localized on a single substructure. A localization length scale is proposed as a measure of the spatial extent of a mode for the purpose of discussing the results of numerical experiments and comparing the localization of different modes. Different modes in the same mode group were found to have significantly different degrees of localization, and similar modes in different mode groups were found to be related to each other via a scaling parameter. Results also indicate that the particular set of random disorder introduced into the finite structure can have a significant effect on the degree of localization.