Tunable band gaps in an inertant metamaterial plate with two-degree-of-freedom local resonance

This article presents an inertant metamaterial plate with two-degree-of-freedom (TDOF) local resonance. It is theoretically investigated with dispersion relation, effective density, and group velocity, and phase velocity to show the unique acoustic performance. Results show that the metamaterial plate can generate two tunable band gaps with a single mass attached by tuning the distance of springs to the centroid of mass due to the extra rotation of the mass. Simultaneously, the band gaps can also be tuned to the lower frequency range by exploiting the inerter. Effective mass density shows negative within the band gaps, and is also tuned by the attached spring-mass and inerter. Finally, within specific frequency ranges, the group velocity is negative which manifests the metamaterial plate behaves abnormal dispersion. (C) 2020 Elsevier B.V. All rights reserved.