Special transformations for pentamode acoustic cloaking

TL;DR

This paper introduces a novel approach to acoustic cloaking by defining desired material properties first and then deriving the transformation functions, enabling specialized cloaks with constant or power-law properties and minimal anisotropy.

Contribution

It inverts the traditional design process by starting with material properties and deriving transformations, facilitating the creation of cloaks with tailored acoustic characteristics.

Findings

Derived transformations for cloaks with constant density and stiffness

Created transformations for power-law material distributions

Achieved cloaks with minimal elastic anisotropy

Abstract

The acoustic cloaking theory of Norris (2008) permits considerable freedom in choosing the transformation function 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 7) minimal elastic anisotropy.