Bandgaps and directional properties of two-dimensional square beam-like zigzag lattices

In this paper we propose four kinds of two-dimensional square beam-like zigzag lattice structures and study their bandgaps and directional propagation of elastic waves. The band structures are calculated by using the finite element method. Both the in-plane and out-of-plane waves are investigated simultaneously via the three-dimensional Euler beam elements. The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges. The effects of the geometry parameters of the xy- and z-zigzag lattices on the bandgaps are investigated and discussed. Multiple complete bandgaps are found owing to the separation of the degeneracy by introducing bending arms. The bandgaps are sensitive to the geometry parameters of the periodic systems. The deformed displacement fields of the harmonic responses of a finite lattice structure subjected to harmonic loads at different positions are illustrated to show the directional wave propagation. An extension of the proposed concept to the hexagonal lattices is also presented. The research work in this paper is relevant to the practical design of cellular structures with enhanced vibro-acoustics performance