Enhancement of band-gap characteristics in hexagonal and re-entrant lattices via curved beams

In-plane wave propagation in hexagonal and re-entrant lattices is a widely investigated subject in the literature. Such systems can exhibit many different but limited band structure properties that depend on the topology and geometry of structural members and the lattice itself. This manuscript proposes a novel class of hexagonal and re-entrant lattices with unit cells containing combined straight and curved beams with enhanced band-gap properties. Timoshenko beams are suggested to represent beam members of the lattice and corresponding governing equations are derived. Bloch theorem is applied to study in-plane wave propagation and get the unique dispersion properties of the modified lattices. The influence of a new geometric parameter, the curvature angle of the constituent curved beams is explored for the dispersion characteristics and wave directionality through iso-frequency contours of dispersion surfaces. Enhanced band-gap properties in the context of the generation of new band-gaps and widening of the band-gaps for the cellular lattices with curved beams are promising from the viewpoint of the future design of phononic crystals and metamaterials in their mechanical setup