The low frequency performance of metamaterial barriers based on cellular structures

Abstract

The high sound transmission loss (STL) metamaterials that have been suggested to-date commonly require the introduction of relatively heavy resonating or constraining components which limit the applicability of these solutions in typical noise control applications where it is desirable to minimize the treatment mass at a given STL. Here it is proposed that a panel consisting of an array of cellular unit structures can possess a high STL within a specified low frequency range without an undue mass penalty. The cellular acoustical metamaterial considered comprises a periodic arrangement of unit cells consisting of plates held in a grid-like frame (which itself is unsupported). It is suggested here that such a cellular panel can yield enhanced STL if the unit cell mass is apportioned appropriately between the unit cell plate and the surrounding grid-like frame, the effect being similar to the high STL observed in the low frequency range for a plate clamped along its edges. A finite element-model of a single unit cell was used to predict the normal incidence transmission loss of the periodic array by im-1 posing boundary conditions that enforce spatial periodicity. Two material designs were compared: one in which the densities of the materials used for the unit plate panel and the grid were changed relative to each other, and a second where the relative thicknesses of the unit plate panel and the grid frame were varied. The numerical simulations indicate that benefits can be achieved in either case. However, the design based on density variations appears to be more effective than the approach based on geometry alteration in creating a relatively broad range of low frequency transmission loss enhancement.

Experiments on the low frequency barrier characteristics of cellular metamaterial panels in a diffuse sound field

“…STL values were predicted using a representative unit cell model [9] and the ABAQUS FE code [32]. The geometric dimensions of the models and the elastic properties corresponded to the averaged values of the measured quantities.…”

“…Metamaterials potentially offer solutions that address the challenge of controlling sound transmission with low mass. Prior investigations on relevant metamaterial systems have considered material configurations such as a matrix with embedded resonating elements, typically a heavy mass coated with a soft rubber coating [4,5], membrane-based materials [6,7], and plate based materials [8,9]. Prior studies on acoustic metamaterials for sound barriers were performed employing either analytical or computational methods: for a review see [10].…”

“…In this paper, intensity-based sound transmission loss experiments are described in which planar cellular metamaterials [9], Fig. 4, were subjected to incident sound fields using a reverberation room setup [26,27].…”

“…Finally, experimentally determined STL data for the metamaterial panels were compared to predictions from a unit cell numerical model [9].…”

Acoustic absorption of solid foams with thin membranes

“…23 In the second class of models, on the other hand, the dynamics of the membranes has been considered but the structures are much simpler, with oneor two-dimensional geometries. [25][26][27] A complete model is therefore still needed. A promising direction is the recent work by Venegas and Boutin, on liquid foams, which are constitutively with cells closed by thin membranes.…”