On the wave propagation properties and Poisson's ratio of the Star-3/6 structures

In this study, wave propagation characteristics of the Star-3/6 structures are studied, and the effects of geometric parameters on the wave propagation are analyzed. Especially, Poisson's ratio is studied based on the long wavelength approximation of band structure. The Star-3/6 structures are assembled to be hexagonal and triangular topologies with re-entrant angles. By using the finite element method and Bloch's theorem, the dynamic models of the Star-3/6 structures are established, and the elastic wave behaviors are calculated. The effects of geometric parameters on distribution of band gaps are studied in detail. By applying the long wavelength approximation of band structure, the Poisson's ratio of the macrostructure is predicted, which is also obtained by the commercial finite element software for the comparisons. This paper confirms that the Star-3/6 structures have a positive Poisson's ratio rather than the visual negative Poisson's ratio. Additionally, the isotropic features of the Star-3/6 structures are evaluated by the group velocity. The Star-3/6 structures show effective isotropic features in the low frequency range. As the frequency of elastic waves increases, the propagation speed of elastic waves decreases, and the wave propagation gradually becomes anisotropic.