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Complete delocalization in a defective periodic structure.

Behrooz Yousefzadeh1, Chiara Daraio1

  • 1Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA.

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Summary
This summary is machine-generated.

Stable, completely delocalized responses occur in nonlinear defective periodic structures. Even with defects, all units oscillate in-phase, eliminating localization in free and forced responses.

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Area of Science:

  • Nonlinear dynamics
  • Solid-state physics
  • Mechanical vibrations

Background:

  • Periodic structures often exhibit localized modes due to defects.
  • Understanding defect behavior is crucial for designing robust systems.
  • Nonlinearities can significantly alter system dynamics.

Purpose of the Study:

  • To investigate the existence of stable, completely delocalized response regimes in nonlinear defective periodic structures.
  • To analyze the conditions under which defect-induced localization is eliminated.
  • To explore both free and forced response scenarios.

Main Methods:

  • Numerical simulations of nonlinear periodic structures with one and two defective units.
  • Analysis of system behavior in free (undriven) and forced (damped-driven) response regimes.
  • Derivation of closed-form analytical expressions for complete delocalization onset.

Main Results:

  • Stable, completely delocalized states were observed, characterized by in-phase oscillations of all units with equal amplitude.
  • In free response, localization is eliminated at a critical energy level.
  • In damped-driven systems, complete delocalization occurs above a specific driving amplitude threshold.

Conclusions:

  • Defect-borne localization can be overcome in nonlinear periodic structures, leading to stable, delocalized responses.
  • The phenomenon is controllable via energy levels (free response) or driving amplitude (forced response).
  • Analytical expressions provide a basis for predicting and engineering these delocalized states.