Complete Delocalization in a Defective Periodic Structure
Abstract
We report on the existence of stable, completely delocalized response regimes in a nonlinear defective periodic structure. In this state of complete delocalization, despite the presence of the defect, the system exhibits in-phase oscillation of all units with the same amplitude. This elimination of defect-borne localization may occur in both the free and forced responses of the system. In the absence of external driving, the localized defect mode becomes completely delocalized at a certain energy level. In the case of a damped-driven system, complete delocalization may be realized if the driving amplitude is beyond a certain threshold. We demonstrate this phenomenon numerically in a linear periodic structure with one and two defective units possessing a nonlinear restoring force. We derive closed-form analytical expressions for the onset of complete delocalization and discuss the necessary conditions for its occurrence.
Cite
@article{arxiv.1710.02486,
title = {Complete Delocalization in a Defective Periodic Structure},
author = {Behrooz Yousefzadeh and Chiara Daraio},
journal= {arXiv preprint arXiv:1710.02486},
year = {2017}
}