The low frequency performance of metamaterial barriers based on cellular structures

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 imposing 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.