Membrane- and plate-type acoustic metamaterials with elastic unit cell edges

Abstract

Membrane- and plate-type acoustic metamaterials are thin membranes or plates consisting of periodic unit cells with small added masses. It has been shown in numerous studies, that these metamaterials exhibit tunable anti-resonances with transmission loss values much higher than the corresponding mass-law. However, in most studies it is assumed that the unit cell edges (or grid) of the metamaterial are fixed. This idealised boundary condition is not applicable to real world applications in noise control. Therefore, the acoustic performance of these metamaterials under more realistic circumstances, where the grid structure cannot be perfectly rigid, can be expected to be different. In this contribution, the vibro-acoustic behavior of membrane- and plate-type acoustic metamaterials with a non-rigid grid is investigated. For this purpose, an efficient analytical model is developed to predict the eigenmodes and sound transmission loss of such metamaterials. In this model, elastic unit cell edges are modelled using a grid of Euler-Bernoulli beams and the sound transmission loss can be calculated for oblique incidence. A comparison to FEM simulations shows that the proposed model yields the same results but with a considerably reduced computational effort. The analytical model is then used to discuss the vibro-acoustic properties of the metamaterial, with particular focus on the influence of the mass and stiffness of the grid beams. It is shown that even when a non-rigid grid and diffuse incident sound fields are considered, the transmission loss of the metamaterial exhibits anti-resonances with remarkably high noise reduction values. These anti-resonances can be tuned by choosing appropriate values of the grid parameters. Furthermore, the formation of band gaps in the propagation of bending waves is discussed by investigating the dispersion curves of the metamaterial. The results in this contribution show that membrane- and plate-type acoustic metamaterials can still efficiently reduce low-frequency noise, even when the unit cell edges are not assumed to be fixed. This important finding and the proposed analytical modal can support the utilization of these metamaterials in practical noise control applications.