Vibration Suppression of Metamaterial with Local Resonators Coupled by Negative Stiffness Springs

This paper proposes a metamaterial beam with local resonators coupled by negative stiffness springs. First, a distributed parameter metamaterial beam model with the proposed configuration of coupled local resonators is developed. Due to the introduction of the negative stiffness springs, the system is prone to be unstable. The stability analysis indicates that the infinitely long metamaterial beam becomes unstable as long as the stiffness of the coupling spring becomes negative. For the finitely long metamaterial beam, the stability could be achieved for given negative coupling springs. A parametric study is then conducted to investigate the effects of the number of cells and the lattice constant on the system stability. The transmittance of the finitely long metamaterial beam is calculated. The result shows that due to the restriction on the tunability of the negative stiffness for the proposed metamaterial beam, a certain trade-off is needed for the appearance of the quasi-static vibration suppression region and the enhancement of the main vibration suppression region.