Tunable metamaterial beam using negative capacitor for local resonators coupling

This article presents a theoretical study of a tunable metamaterial beam for low-frequency broadband vibration suppression. First, the mechanism of employing the shunt circuit technique to realize the internal coupling between two adjacent local resonators is introduced. The working principle of the proposed metamaterial beam by integrating the shunt circuit technique is demonstrated. The stability of the proposed metamaterial beam is then analysed, and the corresponding criterion is proposed. Subsequently, analytical models of the proposed metamaterial beam are developed. The band structures and the transmittances are calculated. The analytical study demonstrates the generation of multiple band gaps using a shunt negative capacitance circuit, which is equivalent to a coupling spring. A parametric study is conducted to investigate the effect of the equivalent coupling stiffness on the band gaps and the corresponding suppression regions. It is found that the band gaps are controllable by varying the equivalent coupling stiffness. Finally, to verify the analytical solutions, a finite-element model of the proposed metamaterial beam is developed. The simulation results confirm the existence of multiple band gaps, which are tunable through modification of the negative capacitance. The broadband vibration-suppression ability of the proposed metamaterial beam is thus confirmed.