Localization and delocalization in one-dimensional dynamic systems

Mechanical structures with reasonably periodic variations in impedance, may exhibit wave localization similar to Anderson localization in atomic systems. Several such systems have been investigated by the authors; specifically, beaded strings, membranes and plates with periodic stiffeners attached, and “jungle gyms”. All these exhibit pass and stop bands in the propagation of vibration in the structure and the related spatial localization and delocalization when the periodicity of the impedance discontinuities is disturbed. When the strict periodicity is perturbed, localization and delocalization occur in the pass and stop bands, respectively. It is demonstrated that these effects depend on the interactions between discontinuities