3D bi-stable negative stiffness mechanical metamaterials for bandgap tuning

Abstract A recent topic of interest in dynamics research is bi-stable negative stiffness (NS) mechanical metamaterials that allow for the efficient control of wave propagation and bandgap (BG) tuning. In this study, a three-dimensional bi-stable NS mechanical metamaterial based on fan-shaped inclined beams was developed. It has BGs in multiple directions as well as significant BG tuning capability in specific direction, and the ability to design for multiple geometrical parameters. First, the requirements for NS mechanical metamaterials to achieve bi-stable properties were theoretically investigated. Subsequently, the deformation process of the unit cell of the metamaterial under uniaxial compression and the band structure and vibrational properties of the metamaterial under different steady states were analyzed through a combination of finite element method and experiments. The results showed that the BG range of the bi-stable NS metamaterials in the vertical direction changed with the switching of the steady state, whereas the out-of-plane BG in the horizontal direction remained constant. Therefore, this bi-stable NS mechanical metamaterial could realize modulation of the BG as well as control of wave propagation in multiple directions. In addition, bi-stable NS metamaterials with different angles exhibited different BG ranges. Finally, the vibrational transmittances of the metamaterials were investigated to verify the accuracy of the BG range.