Low-frequency Locally Resonant Band Gap of the Two-dimensional Quasi-zero-stiffness Metamaterials

• Novel two-dimensional (2D) quasi-zero-stiffness (QZS) metamaterials are engineered. • Low-frequency complete band gaps are fulfilled by the 2D QZS metamaterials. • Remarkable tunability (∼32%) is realized by adjusting the pre-compression and added mass. • In virtue of anisotropy, the complete band gap can be tuned. This paper develops a novel type of two-dimensional (2D) locally resonant (LR) metamaterials with quasi-zero-stiffness (QZS) property both in the horizontal and vertical directions. The unit cell, constructed by attaching the 2D QZS resonator onto a square frame, is periodically arranged to form the QZS metamaterial. The QZS property along two directions is realized by design optimization of the elastic elements of the resonator, namely folded slender beams. Furthermore, the dispersion relation of the 2D QZS metamaterial is computed by developing a theoretical model for continuum structure with local resonators. Then, the formation mechanism of the band gap attributed to the local resonance is revealed by eigenmode shapes of unit cell and the displacement fields over the 2D QZS metamaterial. The results show that the lower-frequency complete band gap can be achieved by pre-compressing the 2D QZS resonators and increasing the added mass. Specifically, the starting frequency of the complete band gap can be reduced by 32% owing to the larger pre-compression and added mass. Moreover, the anisotropy of pre-compressions along the horizontal and vertical directions can be utilized to make the complete band gap overlay different ranges of frequency. This study provides an avenue for achieving a low-frequency complete band gap regardless of the incident direction of in-plane wave.