Acoustic Metamaterial Surfaces With Tunable Effective Density

The term “acoustic metamaterials” refers to mechanical structures composed of unit cells of specific geometry, size and orientation, arranged in repeating patterns so as to achieve uncommon macroscopic behavior with respect to acoustic waves. Such structures are characterized by their effective properties and typically possess frequency dependent effective mass density and bulk modulus, the value of which can even be zero or negative at certain frequencies. The research presented in this paper introduces a novel acoustic surface composed of metamaterial unit cells with tunable effective density. Such an acoustic metasurface, constructed by imposing periodic boundary conditions on a matrix of unit cells, is shown to exhibit frequency selectivity. Namely, we have previously shown that a structure which consists of a thin elastic membrane placed in a short tube coaxial with an acoustic duct exhibits resonant behavior of the effective density, and thus can be used as a building block for creating acoustic metamaterials [1]. Results obtained in [1] and [2], related primarily to 1-D acoustic metamaterials, suggest that such a surface can exhibit a number of different behaviours, according to the values of the geometrical parameters of the unit cells as well as the material parameters of the membrane. Such behaviors include bandpass or bandstop filtering with steep roll-off, as well as band pass or bandstop filtering at multiple frequency ranges. Furthermore, we show that these behaviours can be tuned (i.e. that the frequency range at which a particular effect occurs) without any changes to the geometry of the structure or its material parameters if the effective density of the unit cells is controlled by applying appropriate DC voltage bias to membranes made of piezoelectric material, as suggested by the findings in [3]. If the surface is used in a narrow band of frequencies where its effective density is very close or equal to zero, the refractive index of the surface will also be equal to zero. A characteristic property of such zero refractive index surfaces is that the output angle is equal to zero regardless of the incident angle, and thus such a structure can be used to convert spherical acoustic waves to plane waves. Lastly, we analyze an acoustic metasurface with unit cell effective densities tailored in such a way that a gradient index (GRIN) profile, corresponding to an acoustic lens, is obtained [4]. Depending on the specific profile adopted, the lens can be used for bending or focusing acoustic waves. Specifically, we analyze the effect of using a 20-cell wide array of unit cells (in a 2-D finite element modelling simulation) on the radiation pattern of an acoustic point source.