Special transformations for pentamode acoustic cloaking

Abstract

The acoustic cloaking theory of Norris [Proc. R. Soc. London, Ser. A 464, 2411-2434 (2008)] permits considerable freedom in choosing the transformation f from physical to virtual space. The standard process for defining cloak materials is to first define f and then evaluate whether the materials are practically realizable. In this paper, this process is inverted by defining desirable material properties and then deriving the appropriate transformations which guarantee the cloaking effect. Transformations are derived which result in acoustic cloaks with special properties such as (1) constant density, (2) constant radial stiffness, (3) constant tangential stiffness, (4) power-law density, (5) power-law radial stiffness, (6) power-law tangential stiffness, and (7) minimal elastic anisotropy.

Elastic metamaterials and dynamic homogenization: a review

“…The anisotropic densities needed to realize such cloaks could be achieved by using layered fluids [112,113] (see also [114,115]), however, Norris [17] realized that such inertial cloaks suffer from a considerable mass penalty. He presented an alternative route to designing cloaks for acoustic waves based upon pentamode materials [17,116,117]. The existence of different routes to acoustic wave cloaking has been noted in literature [118].…”

Design of arbitrary shaped pentamode acoustic cloak based on quasi-symmetric mapping gradient algorithm

“…7 These findings stimulate an active study recently for this material conceived theoretically 2 decades ago. [8][9][10][11][12] PM material, including conventional fluid as a special case, is defined as an elastic material with only one non-zero eigenvalue of elasticity matrix, and supports only one kind of stress state. By microstructure design, PM material can be made anisotropic in contrast to conventional fluids.…”

A broadband polygonal cloak for acoustic wave designed with linear coordinate transformation

“…[1][2][3][4][5][6][7][8][9][10][11][12] This coordinate-transformation-based method can also be extended to other physical systems, including acoustics. Thus, using the technique named transformation acoustics, [13][14][15][16] acoustic cloaking [17][18][19][20][21][22][23][24][25][26][27][28] can also be achieved. Significant progress has been made to realize the acoustic cloak practically.…”