Design Arbitrary Shaped 2D Acoustic Cloak without Singularity

TL;DR

This paper introduces a novel method for designing 2D acoustic cloaks with arbitrary shapes that avoids singularities by controlling principal stretches during transformation, validated through analytical and numerical simulations.

Contribution

It presents a deformation-based transformation approach to design nonsingular 2D acoustic cloaks with arbitrary geometries, overcoming previous singularity issues.

Findings

Analytical expressions for nonsingular cylindrical cloak parameters

Numerical method for irregular shape cloaks

Validated cloaking performance through simulations

Abstract

A method is proposed to design arbitrary shaped two dimensional (2D) isotropic-inertia acoustic cloaks without singularity. The method is based on the deformation view of the transformation method, where the transformation tensor A is identified as the deformation gradient tensor and the transformed material parameters can be expressed by the principal stretches in the principal system of the deformation. The infinite material parameters of a perfect 2D cloak is induced by an infinite principal stretch in one direction while the other two remains finite at the inner boundary during the transformation. To circumvent this difficulty, for a 2D cloak we can choose the principal stretch perpendicular to the cloak plane to be also infinite but in the same order as the infinite principal stretch in the cloak plane during the transformation, so the transformed material parameters may keep finite. To illustrate this idea, the analytical expressions of nonsingular material parameters for a cylindrical acoustic cloak are given. For the acoustic cloaks with irregular shapes, the numerical method is proposed to evaluate the principal stretches and in turn the nonsingular material parameters. The designed 2D cloaks are validated by numerical simulation.