Non-singular three-dimensional arbitrarily shaped acoustic cloaks composed of homogeneous parts

Abstract

Acoustic metamaterials are artificial materials whose properties can be controlled at will. Acoustic cloaking is an important application. It can make some space acoustically invisible. In this paper, a model of transformation acoustics is proposed for a general tetrahedron. It contains three parts, each with homogeneous properties. Since most cloaks can be approximated by polyhedrons, they can be divided into a series of tetrahedrons. Thus, most cloaks can be built with homogeneous parts. Helmholtz equations are solved for the space with two polyhedral cloaks with COMSOL Multiphysics finite element software. The results show that the cloaks work well in hiding the space acoustically. In the models, all properties of each part are non-singular. Since all the parameters affect the properties of each part and some also affect the performance of cloaking, a balance can be found between performance and properties. It provides an easier and more realizable way to fabricate acoustic cloaks.

Non-Singular Homogeneous Polyhedral Heat Cloak and Its Realization

“…2 we show a regular tetrahedral cloak presented by Ref. [53], where the shaded domain denotes the designed domain (cloaking domain) while tetrahedron OA 1 B 1 C 1 represents the domain to be cloaked (cloaked domain). For clarity, we select the edge OA 2 to be along the x-axis, and the face OA 2 B 2 in the xoy plane.…”

“…In Ref. [53], the transformation for a tetrahedron cloak is completed by multi-steps. The three segments should be mapped in a specific order as the latter transformation step is dependent on the former one.…”

“…It is known that an arbitrary shaped cloak can be approached by polyhedra, but a quantitative analysis based on this approximation was rarely considered. [50][51][52][53] We first show how cloaks with curved boundaries (regular spherical cloak and cylindrical cloak as illustrative cases here) are approximated by polyhedra and we demonstrate the good cloaking performances of the approximated cloaks. For non-regular shaped cloaks, the convergence behavior in homogenization process hasn't been studied, and this paper primarily focuses on this problem.…”

“…extended these works to three dimensions and proposed a multistep transformation approach for a tetrahedral cloak. 53 However, in Li's nice work, the transformation for a tetrahedral cloak is realized in three steps. The transformation should be conducted in a certain order as the later transformation step is dependent on the former one.…”

Non-closed acoustic cloaking devices enabled by sequential-step linear coordinate transformations

“…Cloaks based on linear coordinate transformation have homogeneous constitutive parameters with finite anisotropy, which obviates the need for space dependent materials. So far, in addition to huge amount of theoretical investigations to advance of cloaks [24][25][26][27][28] , several studies experimentally demonstrated acoustic carpet cloaks via homogeneous fluid-like materials. For example,…”