Wave propagation in two-dimensional periodic lattices

A. S. Phani, J. Woodhouse, N. A. Fleck

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371 Citations (Scopus)

Abstract

Plane wave propagation in infinite two-dimensional periodic lattices is investigated using Floquet-Bloch principles. Frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies: hexagonal honeycomb, Kagome lattice, triangular honeycomb, and the square honeycomb. These topologies exhibit dramatic differences in their long-wavelength deformation properties. Long-wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices. The slenderness ratio of the constituent beams of the lattice (or relative density) has a significant influence on the band structure. The techniques developed in this work can be used to design lattices with a desired band structure. The observed spatial filtering effects due to anisotropy at high frequencies (or short wavelengths) of wave propagation are consistent with the lattice symmetries.
Original languageEnglish
Pages (from-to)1995-2005
Number of pages11
JournalJournal of the Acoustical Society of America
Volume119
Issue number4
Publication statusPublished - Apr 2006

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    Phani, A. S., Woodhouse, J., & Fleck, N. A. (2006). Wave propagation in two-dimensional periodic lattices. Journal of the Acoustical Society of America, 119(4), 1995-2005.