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Acoustic scattering from phononic crystals with complex geometry.

Jason A Kulpe1, Karim G Sabra1, Michael J Leamy1

  • 1School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.

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Summary
This summary is machine-generated.

This study presents a new method for calculating acoustic scattering from phononic crystals (PCs) of any shape. The technique simplifies complex surfaces into facets, enabling efficient computation of external acoustic fields, particularly within bandgaps.

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Area of Science:

  • Acoustics
  • Materials Science
  • Condensed Matter Physics

Background:

  • Phononic crystals (PCs) offer unique acoustic properties.
  • Calculating acoustic scattering from complex PC geometries is challenging.
  • Existing methods may struggle with arbitrary shapes and large numbers of inclusions.

Purpose of the Study:

  • To develop a novel formalism for computing external acoustic scattering from phononic crystals with arbitrary exterior shapes.
  • To enable efficient analysis of acoustic wave interactions with complex PC structures.
  • To provide a validated method for predicting the acoustic response of phononic crystal devices.

Main Methods:

  • Utilizes a Bloch wave expansion technique combined with the Helmholtz-Kirchhoff integral (HKI).
  • Approximates complex PC surfaces as a collection of facets, treating each as a semi-infinite plane.
  • Incorporates wave modes introduced by facets into the HKI to determine the scattered acoustic field.

Main Results:

  • The formalism efficiently computes external acoustic fields for phononic crystals of arbitrary shape.
  • Accurate scattering predictions are achieved, especially within complete bandgaps, avoiding complex internal multiple scattering calculations.
  • Numerical examples for spherical and bean-shaped PCs with over 100,000 inclusions validate the approach.

Conclusions:

  • The facet formalism provides a computationally efficient and accurate method for external acoustic scattering from phononic crystals.
  • This approach is particularly advantageous for analyzing phononic crystal devices operating within their bandgaps.
  • The method is validated against existing techniques, demonstrating its reliability for complex geometries.