Complete Delocalization in a Defective Periodic Structure

TL;DR

This paper demonstrates the existence of stable, fully delocalized wave responses in nonlinear defective periodic structures, showing how defect localization can be eliminated through specific energy levels or driving amplitudes.

Contribution

It introduces the concept of complete delocalization in defective nonlinear periodic structures and provides analytical conditions for its occurrence.

Findings

Complete delocalization occurs at specific energy levels in free systems.

Driving amplitude beyond a threshold induces delocalization in damped-driven systems.

Analytical expressions for the onset of delocalization are derived.

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.