摘要： An investigation of Poisson’s ratios and band gap behaviors of 2D hierarchical re-entrant lattice structures is conducted using finite element method (FEM). The structure with a hierarchy order n (n≥1) is constructed by replacing each outmost vertex of the re-entrant octagons of a hierarchical structure of hierarchy order n?1 with a smaller self-similar re-entrant octagon. The dispersion relation and transmission spectrum of the proposed hierarchical structures are analyzed based on the Bloch’s theorem. The effects of geometrical parameters, order of rotational symmetry and orientation angle of some types of re-entrant polygon cores on the lattice Poisson’s ratio and band gap structures are also investigated. Results show that the re-entrant structures with first order hierarchy exhibit a wider band gap and a stronger attenuation effect compared with structures without structural hierarchy. The first order 2D hierarchical re-entrant structure with a negative Poisson’s ratio of ?0.032 exhibits the widest band gap, 17.8% wider than that of the zeroth order 2D re-entrant structure. The order of rotational symmetry and the orientation angle of the re-entrant polygon cores of the lattice have a strong impact on the lattice Poisson’s ratio and band structures.