Three-dimensional quasi-zero-stiffness metamaterial for low-frequency and wide complete band gap

This paper presents a new class of locally resonant (LR) metamaterials with quasi-zero stiffness (QZS) in three dimensions. The monolithic QZS property is achieved by optimizing the three-dimensional (3D) resonator. For the proposed 3D QZS metamaterial, the characteristics of wave propagation are investigated. A lumped-mass-spring model is developed for 3D continuous elastic matrix with local resonators to theoretically derive the dispersion relation. The eigenmode shapes of the unit cell and the dynamic responses of the 3D QZS metamaterials are achieved to reveal the formation mechanism of low-frequency complete band gap. Results indicate that both the starting and ending frequencies of complete band gap can be declined with the increase of pre-compression or added mass. In addition, adjacent LR band gaps overlap with each other to form a wide band gap by tailoring the proof masses of 3D resonators and operating a reasonable arrangement of multiple local resonators. Therefore, this study provides a feasible approach for opening a low-frequency and wide complete band gap, which enables excellent performance of vibration attenuation regardless of the excitation direction.