Phononic crystals are elastic structures with periodic modulation of material properties like shear modulus and density. Propagation of waves through these periodic systems is affected by reflection, transmission, and interference, which are also influenced by the symmetries of the phononic crystal. The dispersion of waves can be described by a band diagram, where band crossings represent degeneracies in the wave propagation, while bandgaps correspond to the ranges of disallowed wave frequencies. In this project, we exploit the representation theory of planar symmetry groups developed for hard condensed matter systems to predict how the band crossings and gaps in the band diagram are affected by the symmetries of a phononic crystal. These theoretical predictions were confirmed by numerical calculations of the band diagrams for 2D phononic crystals exhibiting different planar symmetries.  Hence, we can explain how band diagrams change in response to the symmetry breaking of phononic crystal induced by external loads, which has implications for tunable sound filters and waveguides. 

Effect of Crystal Symmetries on Wave Propagation through 2D Phononic Crystals

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