Design and analysis of gradient quasi-zero stiffness metamaterial isolator with continuous stepped plateau for anti-perturbations

Conventional quasi-zero stiffness (QZS) isolators are highly sensitive to the load they bear, and typically have strict requirements for the applied load. A novel gradient QZS isolation metamaterial with continuous stepped QZS plateau in its load–displacement curve is proposed in this paper, which is designed to resist perturbations. To establish the connection between the gradient configuration and the load–displacement curve with a continuous stepped QZS plateau, this paper first proposes a design method for the QZS unit cell. The unit cell is composed of compliant constant-force curved beams, and a chained beam constraint model based on B-spline curves is proposed to solve its large deformation problem. The factors affecting the load–displacement curve of the compliant curved beam are analyzed. Then, an optimization algorithm is used to achieve a gradient arrangement of the unit cells in the vertical direction of the metamaterial, in order to realize the continuous stepped QZS plateau characteristics of its load–displacement curve and broaden the range of effective isolation load intervals. Finally, the vibration transmissibility of the gradient QZS metamaterial isolator in the presence of load perturbations was derived using the harmonic balance method. The results indicate that the presence of load perturbations can have a negative impact on the low-frequency or ultra-low-frequency isolation band. The design of a gradient QZS metamaterial isolator with a continuous stepped QZS plateau can mitigate this negative effect.