Building and Destroying Symmetry in 1-D Elastic Systems

Locally periodic rods, which show approximate invariance with respect to translations, are constructed by joining $N$ unit cells. The spectrum then shows a band spectrum. We then break the local periodicity by including one or more defects in the system. When the defects follow a certain definite prescription, an analog of the Wannier-Stark ladders is gotten; when the defects are random, an elastic rod showing Anderson localization is obtained. In all cases experimental values match the theoretical predictions.