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Localization in semi-infinite herringbone waveguides.

S G Haslinger1, I S Jones2, N V Movchan1

  • 1Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK.

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Summary
This summary is machine-generated.

This study analyzes wave scattering in a specialized plate waveguide. Novel results predict how flexural waves localize around rigid pins in a herringbone pattern.

Keywords:
Kirchhoff plateflexural wavesherringbone systemslocalizationplatonic crystals

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Area of Science:

  • Solid Mechanics
  • Acoustics
  • Wave Propagation

Background:

  • Wave scattering and localization phenomena are crucial in understanding material behavior under dynamic loads.
  • Elastic plates with embedded structures present complex wave interaction challenges.
  • Herringbone patterns offer unique geometric configurations for wave manipulation.

Purpose of the Study:

  • To investigate the scattering and localization of time-harmonic flexural waves.
  • To model wave interaction with a semi-infinite herringbone waveguide of rigid pins in an elastic Kirchhoff plate.
  • To analyze the influence of pin orientation and spacing on wave behavior.

Main Methods:

  • Development of an analytical model for wave propagation in the structured plate.
  • Incorporation of dipole approximations for closely spaced pins.
  • Theoretical analysis and simulation of localized waveforms.

Main Results:

  • Novel results on the scattering and localization of flexural waves by the herringbone waveguide.
  • Demonstration of how pin geometry affects wave scattering patterns.
  • Prediction of localized waveform characteristics.

Conclusions:

  • The analytical model accurately predicts flexural wave scattering and localization in the studied system.
  • Herringbone waveguide geometry significantly influences wave dynamics.
  • The findings contribute to the understanding of wave manipulation in structured elastic media.