Wave characteristics of two-dimensional hierarchical hexagonal lattice structures

Hierarchical structures are structures that themselves contain structural elements. Hierarchical lattice structures are counterparts of the traditional lattice structures, whose walls are replaced by some kind of structure. In this paper, wave propagation in two-dimensional hierarchical hexagonal lattice structures is calculated by the finite element method with the Bloch theory. Attention is devoted to the comparison of the band gap, wave mode, dispersion surface, and phase and group velocities between the second-order hierarchical hexagonal lattice structures and their first-order traditional counterpart. The results show that the former structures have more band gaps and similar isotropic wave behavior in the low frequency compared to the latter structure. The structure hierarchy is favorable for the periodic lattice structure to filtering or guiding wave at some circumstances to meet the demands of engineering.