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arXiv · 1710.02486

Complete Delocalization in a Defective Periodic Structure

Behrooz Yousefzadeh·Chiara Daraio
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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.

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Behrooz Yousefzadeh, Chiara Daraio. 2017-10-06. Complete Delocalization in a Defective Periodic Structure. https://doi.org/10.1103/physreve.96.042219

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