Vibration Localization by Disorder in Assemblies of Monocoupled, Multimode Component Systems

Abstract

Disorder in nominally periodic engineering structures results in the localization of the mode shapes to small geometric regions and in the attenuation of waves, even in the passbands of the corresponding perfectly periodic system. This paper investigates, via probabilistic methods, the transmission of steady-state harmonic vibration from a local source of excitation in nearly periodic assemblies of monocoupled, multicomponent mode substructures. A transfer matrix formulation is used to derive analytical expressions for the localization factor (the rate of exponential decay of the vibration amplitude) in the limiting cases of strong and weak modal coupling. The degree of localization is shown to increase with the ratio of disorder strength to modal coupling. The increase is nearly parabolic for small values of this ratio, and logarithmic for large values. Furthermore, the localization factor increases very rapidly with the passband number. Typically, the transition from weak to strong localization occurs from one passband to the next, and severe vibration confinement is unavoidable at high frequencies, even for very small disorder.