Wave propagation in hexagonal and re-entrant lattice structures with cell walls of non-uniform thickness

On the basis of the Blochs theorem, the in-plane wave propagation in hexagonal and re-entrant lattice structures with cell walls of non-uniform thickness is investigated using the dynamic stiffness matrix in conjunction with the Wittrick-Williams algorithm. Special attention is devoted to the effects of the internal angle, the slenderness ratio and the material distribution on the directional and band gap behaviors. Results show that the three considered parameters can significantly influence the band gap characteristics. For the wave propagation directionality, however, the internal angle is more prominent than the other two factors. The work expects to serve as a guide for the optimal design of directional mechanical filters.