Design and compression-induced bandgap evolution of novel polygonal negative stiffness metamaterials

The paper proposes a novel polygonal negative stiffness (NS) metamaterial composed of folded beams and stiffening walls, which exhibits excellent performance in attenuating waves over a broad frequency range and shows compression-induced bandgap evolution characteristics. Dispersion relation and bandgaps for the propagation of elastic waves in NS metamaterials are calculated utilizing a semi-analytical periodic spectral method (PS-SAFE). The results demonstrate that broadband bandgaps can be achieved in the proposed polygonal NS metamaterials. Mode analysis and transmission spectrum are utilized to explain the underlying mechanisms of wave attenuation. Furthermore, appropriate deformation conditions are applied to the NS metamaterials to realize compression-induced bandgap evolution, which shows that compression-induced configuration variations significantly impact the frequency range and bandwidth of the bandgaps. As the deformation increases, folded beams enter the elastic instability stage, and the internal stress change strongly influence the vibration displacement modes, leading to various symmetric and antisymmetric displacement vibration modes within a similar frequency range, forming low-frequency broadband bandgaps. This work provides valuable insights into the design of advanced materials for low-frequency broadband wave attenuation.