Broad bandgap active metamaterials with optimal time-delayed control

Abstract

In this paper, a metamaterial with time-delayed feedback control for broadband vibration suppression is investigated. Genetic algorithm is used to optimize the time-delayed feedback controller to achieve low broadband vibration suppression and even full frequency vibration suppression. Time-delayed feedback controller is introduced between the visible and internal masses of the metamaterial. Time-delayed control tunes the bandgap of the metamaterial and achieves broadband tunable vibration suppression. To further broaden the bandgap, a supercell model with time-delayed control is established, and the time-delayed controller is optimized using the genetic algorithm to determine the optimal control gain and time delay. Two optimization schemes with different objectives are designed. Optimization I: Achieve the widest bandgap at the target attenuation rate. Optimization II: Achieve the maximum attenuation rate in the target frequency range. The results show that multiple bandgaps can be coupled to achieve the widest bandgap at the target attenuation rate. The controller is optimized over the full frequency band to achieve the maximum attenuation rate. Numerical results verify that the metamaterial with optimal controller can achieve vibration suppression over the full frequency range.