Design and numerical validation of quasi-zero-stiffness metamaterials for very low-frequency band gaps

A novel one-dimensional quasi-zero-stiffness (QZS) metamaterial is proposed to acquire very low-frequency band gaps. The representative unit cell (RUC) of the QZS metamaterials is constructed by combining positive-stiffness (PS) elements (two pairs of folded beams) and negative-stiffness (NS) elements (two pairs of buckled beams) in parallel. The negative stiffness of the buckled beams under large deformation is predicated theoretically by using the elliptic integral method. A parameter design on both the PS and NS elements is carried out, which indicates that the positive stiffness can be substantially neutralized by the NS elements, leading to a QZS RUC with ultra-low stiffness. Additionally, the one-dimensional QZS metamaterials are modelled as a lumped-mass-spring chain, which is solved theoretically by using the Harmonic Balance method, and then the dispersion relations and the band gaps are revealed. This chain model is also solved numerically and validated by finite element analysis. Both the theoretical and numerical predictions show very low-frequency band gaps (about 20 Hz). Therefore, the proposed QZS metamaterials should be a promising solution for very low-frequency wave filtering or attenuation.