A novel re-entrant honeycomb metamaterial with tunable bandgap

An auxetic metamaterial consisting of a re-entrant honeycomb structure with hierarchical characteristics (RHS-H) is proposed. The new structure is constructed by attaching small re-entrant structural unit cells to the nodes of the traditional re-entrant structures. Not only can the overall stiffness and stability of the proposed structure be tuned during compression and tension, but a better acoustic performance is also obtained compared with traditional re-entrant honeycomb structures. Firstly, the deformation mechanism of the bandgap is numerically explored by analyzing the dispersion curve of the microstructure as well as the upper and lower bounds of the bandgap vibrational modes. Secondly, the bandgap tunability of the designed structure under uniaxial compression or tension is discussed. Finally, the transmittance of finite period size is calculated to verify the numerical results of the bandgap. Numerical simulation results show that the proposed novel RHS-H has attenuation characteristics of a tunable low-frequency plane wave through a reasonable selection of compressive strain, tensile strain and geometric parameters. The vibration damping strength of the bandgap increases under tensile strain. When the auxetic effect is enhanced, the first and second bandgaps become lower and wider. The novel metamaterial has potential applications in vibration and noise reduction and the design of acoustic devices in dynamic environments, while providing new ideas and a methodology for the real-time adjustment of bandgaps.