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Two-dimensional locally resonant phononic crystals with binary structures.

Gang Wang1, Xisen Wen, Jihong Wen

  • 1Institute of Mechatronical Engineering, National University of Defense Technology, Changsha 410073, China. wang-g@vip.sina.com

Physical Review Letters
|November 5, 2004
PubMed
Summary

This study introduces a lumped-mass method for analyzing elastic wave propagation in phononic crystals. It reveals subfrequency band gaps arising from local resonance in binary periodic systems.

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Area of Science:

  • Materials Science
  • Acoustics
  • Solid Mechanics

Background:

  • Conventional methods struggle with elastic wave propagation in 2D binary periodic systems.
  • Locally resonant phononic crystals offer unique wave manipulation properties.

Purpose of the Study:

  • To apply the lumped-mass method for analyzing elastic wave propagation in 2D binary periodic systems.
  • To investigate the formation of subfrequency band gaps in locally resonant phononic crystals.

Main Methods:

  • Lumped-mass method applied to 2D binary periodic systems (soft rubber/epoxy, vacuum/epoxy).
  • Numerical simulations of phononic crystals with periodic soft rubber cylinders in an epoxy host.
  • Analysis of the locally resonant mechanism using 2D models and quasi-1D analogs.

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Main Results:

  • The lumped-mass method effectively analyzes elastic wave propagation where conventional methods fail.
  • Subfrequency band gaps are predicted due to high contrast in mass density and elastic constants.
  • A criterion is established to determine if resonant modes create subfrequency band gaps.

Conclusions:

  • The lumped-mass method is a viable approach for studying complex phononic crystal systems.
  • Local resonance is a key mechanism for generating subfrequency band gaps.
  • Understanding this mechanism allows for the design of materials with tailored acoustic properties.