Enhanced attenuation band in active 2D mass-in-mass metamaterial using static output feedback

Abstract

Active feedback control is implemented between the inner and outer masses of a 2D mass-in-mass metamaterial to widen the attenuation bandwidth by reducing the displacement of the outer mass of each unit cell. The optimal static output feedback control is applied to a single representative unit. The gain is computed from the analysis of a single unit cell and further used along with the Bloch–Floquet theorem for obtaining the dispersion relationship for an infinite 2D discrete square lattice metamaterial. The proposed model is validated by comparing the results against the finite element simulation in ANSYS. The control gain couples the displacements and velocities, which generates the damping phenomenon even in an undamped system. The controller design requires feedback of only a few measured output instead of all the state variables, and offline computation of the feedback gains reduces the time delay. Effective mass analysis and energy dissipation mechanism are performed which sheds light on the physics underlying the attenuation phenomena. An ultra-wide uninterrupted attenuation band can be perceived as the negative effective mass region significantly extends beyond the standard limit by employing the active feedback control. Additionally, the attenuation bandwidth exists in the low frequency due to the damping induced from the active control.