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Published October 2017 | Submitted + Published
Journal Article Open

Complete delocalization in a defective periodic structure


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.

Attached Files

Published - PhysRevE.96.042219.pdf

Submitted - 1710.02486.pdf


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August 19, 2023
October 17, 2023