Acoustic cloaking using layered pentamode materials

Abstract

While receiving less attention in the literature than electromagnetic cloaking, theoretical efforts to define and create acoustic cloaks based upon mimicking coordinate transformations through use of metamaterials is of interest. The present work extends recent analysis of Norris [Proc. R. Soc. London, Ser. A 464, 2411-2434 (2008)] by considering a range of cloaks, from those comprised of fluid layers which are isotropic in bulk moduli with anisotropic density to those having anisotropic bulk moduli and isotropic density. In all but pure inertial varieties, fluid layers comprising the cloaks are pentamode materials governed by a special scalar acoustic equation for pseudopressure derived by Norris. In most cases presented, material properties of the fluid/pentamode layers are based upon target values specified by continuously varying properties resulting from theoretical coordinate transformations geared to minimize scattered pressure limited by realistic goals. The present work analyzes such cloaks for the specific case of plane wave scattering from an acoustically hard sphere. An initial exploration of the parameter space defining such cloaks (for example, material properties of its constituent layers, and operating frequency) is undertaken with a view toward "optimal" design.

On the practicability of pentamode mechanical metamaterials

“…In two dimensions or in thin plates, usual anisotropic elastic materials can suffice [4,5,6]. In three dimensions, one either needs materials with anisotropic mass density tensors [3,7,8,9] or pentamode materials [3,10,11,12] to implement the counterpart of invisibility cloaks or other devices. Neither of these materials has been realized experimentally so far.…”

Fluid Flow Control with Transformation Media

“…The key idea that enabled progress in those areas was the combination of coordinate transformations with coordinate-dependent, and often extremely exotic [5,[13][14][15], material properties. Transformation optics [3][4][5]11,16] and transformation acoustics [6-8] offer solutions to some inverse scattering problems [17] by reducing them to an elementary one-for example, scattering off a point object in free space.There is no reason why this conceptual approach cannot be used in other areas of physics [18], and, in fact, it has already been applied to conductive heat transfer [19], linear elastodynamics [5,8,[20][21][22][23][24], surface wave [25], and quantum-mechanical matter wave [26] dynamics. The fundamental requirement for the applicability of this concept is the presence of a medium with sufficiently flexible properties, which enables manipulation of the coefficients in the equations describing the dynamical process.…”

“…There is no reason why this conceptual approach cannot be used in other areas of physics [18], and, in fact, it has already been applied to conductive heat transfer [19], linear elastodynamics [5,8,[20][21][22][23][24], surface wave [25], and quantum-mechanical matter wave [26] dynamics. The fundamental requirement for the applicability of this concept is the presence of a medium with sufficiently flexible properties, which enables manipulation of the coefficients in the equations describing the dynamical process.…”

Broadband acoustic concentrator with multilayered alternative homogeneous materials

“…7 Scandrett et al demonstrated acoustic cloaks can constructed by using layered pentamode-type fluids. 8 All these theories and experiments demonstrate that the optical and acoustical coordinate transformations can be used to manipulate, restrict, and control the flow of energy, in the form of either EM waves or acoustic waves.…”