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Wave propagation in two-dimensional periodic lattices.

A Srikantha Phani1, J Woodhouse, N A Fleck

  • 1Department of Engineering, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, United Kingdom.

The Journal of the Acoustical Society of America
|April 29, 2006
PubMed
Summary

This study explores wave propagation in 2D periodic lattices, revealing how lattice design impacts frequency bandgaps and spatial filtering. Understanding these properties allows for the design of specialized acoustic and mechanical metamaterials.

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Area of Science:

  • Solid mechanics
  • Acoustics
  • Materials science
  • Wave physics

Background:

  • Periodic structures exhibit unique wave propagation characteristics, including bandgaps.
  • Floquet-Bloch theory is a powerful tool for analyzing wave phenomena in periodic media.
  • Lattice topology significantly influences mechanical and acoustic properties.

Purpose of the Study:

  • Investigate plane wave propagation in infinite 2D periodic lattices.
  • Examine frequency bandgaps and spatial filtering in various lattice topologies.
  • Relate lattice design parameters to wave propagation behavior.

Main Methods:

  • Application of Floquet-Bloch principles for wave analysis.
  • Numerical investigation of four distinct planar lattice topologies: hexagonal honeycomb, Kagomé, triangular honeycomb, and square honeycomb.

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  • Comparison of numerical results with homogenization theory for long-wavelength behavior.

    • Main Results:

    • Significant differences in long-wavelength deformation properties were observed across the four lattice topologies.
    • Homogenization theory accurately predicted long-wavelength asymptotes of dispersion curves.
    • The slenderness ratio of constituent beams critically influences the band structure.
    • Spatial filtering effects at high frequencies correlate with lattice symmetries.

    Conclusions:

    • Lattice topology and constituent beam properties dictate wave propagation characteristics, including bandgaps and filtering.
    • The developed techniques enable the design of lattices with tailored band structures for specific applications.
    • Anisotropic spatial filtering at high frequencies is a direct consequence of lattice symmetries.