Analysis of in-plane wave propagation in hexagonal and re-entrant lattices

Plane wave propagation in hexagonal and re-entrant lattices is investigated through the application of Bloch's theorem. Two-dimensional dispersion relations are estimated and analyzed to illustrate peculiar properties of re-entrant configurations and investigate the directional behavior of hexagonal lattices for varying construction angles. Special attention is devoted to the determination of phase and group wave velocities. Velocity plots are obtained for varying frequency and direction of wave propagation to analyze the dispersion characteristics of the lattices and further investigate their directional characteristics.