Rotating, cylindrical, acoustic invisibility cloak: solution using perturbation method

TL;DR

This paper investigates the performance of a 2D cylindrical acoustic invisibility cloak under rotation, using perturbation and numerical methods, revealing that rotation degrades cloaking effectiveness.

Contribution

It introduces a perturbation-based approach to analyze rotating acoustic cloaks, providing a fast and accurate evaluation method for their performance under realistic conditions.

Findings

Rotation reduces cloaking performance with increased scattering.

Perturbation and numerical methods agree within 5%.

Perturbation method is computationally efficient.

Abstract

Transformation Acoustics emerged in the mid-2000s, initiating a new paradigm of metamaterial designs. One of the most compelling designs, the invisibility cloak, holds promise for stealth and noise reduction applications in aviation. However, adapting this design to meet the demands of realistic conditions has proven challenging. This work focusses on the design of a stationary 2D cylindrical cloak and its performance whilst rotating, a result not yet reported in the literature. The study utilises linearised equations of motion with convective terms. A wave equation is derived, and corresponding solution and scattering coefficient are derived using a perturbation method and exact numerical solution. These results are used to evaluate the performance of the rotating cloak. Results show that rotation causes a reduction in cloaking performance with greater scattering observed for increasing rotational speeds, with a reasonable agreement (within 5%) between methods over the range of applicability. The perturbation method offers a fast, computationally inexpensive means of evaluating a rotating, graded anisotropic fluid.