Acoustic characteristics of damped metamaterial plate with parallel attached resonators

Abstract

An acoustic metamaterial consisting of a homogeneous damped plate with parallel attached resonators is presented. Theoretical analysis shows that the metamaterial plate can generate multiple resonant-type band gaps and the lower-bound frequency of each band gap coincides with the resonance frequencies of the resonators. The parallel arrangement of resonators, compared with the metamaterial plate with resonators attached in series reported by Peng et al. (2015), results in a wider second band gap with a lower edge, while the first band gap is almost the same, creating therefore an easier combination of the multiple band gaps into a wider one. It is noted that damping has a significant influence on the band gaps and the effective mass density (especially for the damping of resonators). Specifically, it can be concluded that damping cannot be neglected in practical engineering applications, damping in the material of the host plate can smooth and lower the responses in the whole frequency range, especially in the higher frequency range, and a high level of damping of resonators deactivates the effect of band gaps. Such weak/damped resonators actualise the metamaterial damping poorly, and rather tend only to contribute to the overall damping such as the damping of the host plate.