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Published October 2017 | Submitted + Published
Journal Article Open

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 we discuss the necessary conditions for its occurrence.

Additional Information

© 2017 American Physical Society. Received 8 August 2017; published 30 October 2017. B.Y. was supported by a postdoctoral fellowship from the National Science and Engineering Research Council of Canada. This material is based upon work supported by the National Science Foundation under EFRI Grant No. 1741565.

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Published - PhysRevE.96.042219.pdf

Submitted - 1710.02486.pdf

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Created:
August 19, 2023
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October 17, 2023