Longitudinal wave attenuation and bandgap analysis of a novel type hybrid tunable resonator metamaterial

Achieving vibration suppression or wave attenuation of tunable local resonance metamaterials without physical modification of the resonator has received a lot of attention recently. In this paper, a hybrid tunable metamaterial with a resonator containing a lever mechanism, an electromagnetic device, and a feedback system is proposed to achieve tunable bandgap and longitudinal wave attenuation. Unlike ordinary metamaterials, inertial amplification mechanisms and negative stiffness elements are involved in our proposed metamaterials. The function of the electromagnetic device and the feedback control are considered to theoretically derive the dispersion relation. The effective mass, the effective stiffness, the displacement transmission rate, and the band structure of the proposed metamaterial are analyzed, and the contributions of some key parameters on the bandgap are investigated. The accuracy of the analytical band structure is verified by the wave transmittance curves obtained by numerical simulation and the transient displacement response of a single oscillator. The results show that the proposed metamaterial yields broadband tunable bandgap in the low-frequency range, which enables the isolation of low-frequency longitudinal vibrations. This study provides a novel option for constructing integrated metamaterials to achieve vibration suppression and wave attenuation.