Metamaterial beam with resonators of active feedback control to broaden and tune the bandgaps

Broadening and tuning the bandgap properties are important for the application of locally resonant metamaterials. However, the bandgap of classical locally resonant metamaterials is generally narrower. In this paper, a locally resonant metamaterial beam with active feedback control systems is proposed to broaden and tune the bandgap. The dispersion relation and transmissibility of the active control locally resonant metamaterial beam are obtained via the spectral element method and finite element method. The results show that the lower limit of locally resonant bandgap moves to lower frequency; meanwhile, the upper limit of locally resonant bandgap moves to higher frequency with the change of control gain. It breaks the restriction of locally resonant bandgap frequency range moving to higher frequency or lower frequency at the same time. The frequency range of the bandgap is greatly broadened. The locally resonant and Bragg bandgaps are coupled to form a broad bandgap by tuning the control gain and introducing damping. The metamaterial with damping can achieve vibration suppression over a wider frequency range. Vibration suppression over a wide frequency range is verified via the finite element method. The control robustness analysis is verified by considering the effects of noise and stiffness deviation on the system. This paper provides a novel method for broadband vibration suppression.