Ultra-wide bandgap in active metamaterial from feedback control

To widen the attenuation bandwidth in a mass-in-mass metamaterial chain, active feedback control is employed within the unit cell. The optimal control via Linear Quadratic Regulator is used to ensure the stability of the solution as well as adaptive tuning of the system. The key concept is to obtain a wider bandwidth by reducing the displacement amplitude of the outer mass of each unit of the metamaterial. Transmittance for finite number of units and dispersion diagram for infinitely long metamaterial chain are obtained using the backward-substitution method and Bloch-Floquet's theorem, respectively. Results evidenced that an ultra-wide uninterrupted attenuation band starting from very low free wave frequency can be obtained. The dispersion diagram primarily depends on the frequency ratio of the resonating unit with the external main unit. The effect of the mass ratio is insignificant while active feedback control is implemented. This unique phenomenon implies that for a very low mass ratio also a wider bandwidth can be achieved. This enables to design a lightweight structure having wider bandwidth in low-frequency regime.