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In this paper, the wave propagation in phononic crystal composed of auxetic star-shaped honeycomb matrix with negative Poisson's ratio is presented. Two types of inclusions with circular and rectangular cross sections are considered and the band structures of the phononic crystals are also obtained by the finite element method. The band structure of the phononic crystal is affected significantly by the auxeticity of the star-shaped honeycomb. Some other interesting findings are also presented, such as the negative refraction and the self-collimation. The present study demonstrates the potential applications of the star-shaped honeycomb in phononic crystals, such as vibration isolation and the elastic waveguide.

In this paper, vibration and wave propagation characteristics of auxetic metamaterial of the star-shaped structure system are studied. The plane wave expansion method is adopted to investigate and calculate the band structures of the auxetic star-shaped structure system. Besides, the frequency ranges of the complete bandgaps are also obtained and discussed. Then, the COMSOL® finite element software is utilized to solve wave propagation characteristics within the periodic auxetic star-shaped honeycomb structures. After that, the auxetic star-shaped structure devices made by 3D printed machine are used to measure the experimental results and also compared with numerical results. It can be seen that good agreements can be found in the discussions.