Active Metadamping: A phenomenon of damping enhancement in metamaterial via feedback control

Metadamping is defined as the enhancement of dissipation (or the damped response) of an acoustic metamaterial over an equivalent phononic crystal for the same amount of prescribed damping.The emergence of metadamping and decay coefficient in conjunction with active feedback control is the prime novelty of this paper. The wave-number-dependent active metadamping is defined as the difference between the damping ratio of the active-controlled and that of the uncontrolled metamaterial to indicate its improved energy dissipation. The controller design is based on the Linear Quadratic Regulator with output feedback of velocity, and displacement as well as velocity. The damping emergence metric over the entire Brillouin zone is obtained from the dispersion relationship by applying Bloch's theorem, and a parametric study is performed to get an insight into the metadamping phenomenon. Velocity feedback control (VC) provides the highest value of total damping ratio when compared to the case of displacement-and velocity-based feedback control (DVC) for an identical long wave sound speed; however, at the expense of reduced attenuation bandwidth. The decay coefficient of DVC is higher compared to that of VC up to a threshold of long wave speed of sound. Beyond that threshold, both VC and DVC provide almost equal decay. We identified the possibility of obtaining high damping in a stiff metamaterial via active control, which will be useful for applications in the field of vibrations and acoustics, impact mitigation, shock absorption, and vehicle dynamics.

Automated summary

This paper introduces the concept of metadamping and its application in acoustic metamaterials. The use of active feedback control enhances the energy dissipation capability of the metamaterials. The study shows that velocity feedback control provides the highest total damping ratio, but at the expense of reduced attenuation bandwidth. Additionally, it is possible to achieve high damping in stiff metamaterials through active control.