Research on coordinate transformation design of a cylinderical acoustic cloak with pentamode materials

Abstract

The pentamode material, similar to fluid in physical properties, serves as a useful way for the physical implementation of the anisotropic fluid. Based on the similarity, a method to design cloak with the pentamode materials has been put forward by Norris. To analyze the effect factors and rules of the stealth performance of the cloak, the present article is focused on the studying of the coordinate transformation equation of the pentamode cloak design of Norris. Cloaks with different materials parameters distribution can be achieved by adjusting coordinate transformation equations. There are four kinds of the distribution of pentamode cloak material parameters: the density equation being constant, the modulus equation being constant, the density equation being, power equation and the modulus equation being power equation. The average visibility is considered as the standard of stealth effect and is calculated with different coordinate transformation equations by using the software COMSOL. The average visibility is used to analyze the relationship between stealth effect and coordinate transformation equations. The relationship between the coordinate transformation equation and the route of acoustic wave transmission, the relationship between the materials of obstacle and the stealth effect, and the relationship between the route of acoustic wave transmission and the stealth effect are studied. Two results are achieved by comparing these relationships mentioned above. The first is that the stealth effect of a cloak with aluminum obstacle is worse than one with water obstacle. The reason lies in the impedance mismatch between the aluminum and the cloak material. The second result shows that the coordinate transformation equation is related to the distribution of material parameters and the route of acoustic wave transmission and it can affect the scattering property of the cloak. When the route of acoustic wave transmission is close to inner surface of cloak, the stealth effect is relatively poor, while when the route of acoustic wave transmission is close to outer surface of cloak, the stealth effect is relatively well. The reason is that when the route of acoustic wave transmission is close to inner surface of cloak, the acoustic wave affects the obstacle which leads to the enhancement of the scattering of obstacle. So when designing the cloak, not only the physical realization of the cloak material but also the distributed situation of the route of acoustic wave transmission should be considered. And the route of acoustic wave transmission is decided by the coordinate transformation equation. Therefore the stealth performance can be improved by applying proper coordinate transformation equation.