Plane Wave Propagation in Two Dimensional Auxetic Periodic Structures

Cellular structures like hexagonal honeycombs have been of particular interest because of their unique dynamic behavior. These periodic structures can control wave propagation through exhibiting pass and stop bands over certain frequency ranges. Geometrical modifications of unit cells in these hexagonal honeycombs have been explored to achieve different properties such as a negative Poisson´s ratio, which is also known as auxetic materials. It is found that a characteristic angle of the unit cell determines the value of the Poisson´s ratio. In this study, we investigate different topologies of unit cells through the Timoshenko beam-based finite element method and the principles of Floquet-Bloch theorem. We find that the characteristic angle of the unit cell has a significant effect on the in-plane wave propagation behavior and its directionality.