Wave propagation in hexagonal lattices with plateau borders

The purpose of this paper is to investigate the plane wave propagation in two-dimensional hexagonal lattices with plateau borders and analyze the effects of the dimensional parameters on the dynamic properties of hexagonal lattices. Based on the Bloch's theorem and the finite element method, the dispersion relations of this structure are analyzed. The band gaps of three different structures are compared to illustrate the advantages of the hexagonal lattices with plateau borders. Effects of the dimensional parameters including the relative density, material distribution parameter and aspect ratio on the wave characteristics of the hexagonal lattices with plateau borders are also studied via the investigations of the gap maps and phase constant surfaces. More stop bands exist in the band structures of hexagonal lattices with plateau borders in comparing dispersion relations of regular hexagonal lattices with uniform thickness and lattices with parabolic thickness. The relative density, material distribution parameter and aspect ratio have significant effects on the wave characteristics of lattice structures. This work is expected to offer new opportunities for the multi-functional design of the hexagonal lattices and future applications in sound insulation devices.