Hierarchical coiled phononic crystals: Reflectionless interfaces by duality

Duality has previously been demonstrated in twisted Kagome lattices, which are composed of a 2-D unit cell whose configuration can be transformed smoothly by varying a particular unit cell parameter. In the Kagome lattice, the twist angle defines the orientation of two triangular structures comprising the unit cell. In this case, duality expresses the fact that dispersion curves are identical for twist angles that are + /− δψ away from the self-dual configuration at ψ;c. The term self-dual refers to a certain unit cell configuration where dispersion curve families become degenerate, and thus, overlap. In this talk, a 1-D phononic crystal (PnC), composed of rotation-locked nodes linked by flexible bars modeled by continuum elements, is studied as a function of a twist angle. Interestingly, we demonstrate that a 1-D bar-based PnC also exhibits duality, when subjected to periodic rotation locking at the nodes. We show that particular segments of dual unit cells, having a + /− 90o difference in their wave propagation axes may be connected together without reflection and that this enables hierarchically coiled PnC (HCPnC), is contrasted with topologically protected metamaterials that also enable reflectionless wave propagation around a corner.