Mode Localization Phenomena in Nearly Periodic Systems

Abstract

The normal mode localization in nearly periodic systems with one-degree-of-freedom subsystems and a single subsystem departing from the regularity in one, two, and three dimensions has been studied. The closed-frequency equations may be derived by using the U-transformation technique. It is shown that in one- and two-dimensional problems any amount of simple disorder (for stiffness or mass), however small, is sufficient to localize one mode and in three-dimensional systems, a finite threshold of disorder is needed in order to localize one mode. These conclusions are in agreement with those predicted by Hodges.