A novel design scheme for acoustic cloaking of complex shape based on region partitioning and multi-origin coordinate transformation

Abstract

Acoustic cloaking is an important application of acoustic metamaterials. This article proposes a novel design scheme for acoustic cloaking based on the region partitioning and multi-origin coordinate transformation. The cloaked region is partitioned into multiple narrow strips. For each strip, a local coordinate system is established with the local origin located at the strip center, and a coordinate transformation in the local coordinate system is conducted to squeeze the material along the strip length direction to form the cloaked region. To facilitate the implementation of the acoustic cloak, the multilayer effective medium is used to approximate the non-uniform anisotropic material parameters. The effectiveness of the proposed coordinate transformation method is verified by comparing the results from our method with those in the literature. Firstly, the results of a circular acoustic cloak in the literature are reproduced by using our finite element (FE) simulations for validation. Then, a comparison is made between the traditional coordinate transformation scheme and our new scheme for simulating an elliptical acoustic cloak. The results indicate that the proposed multi-origin coordinate transformation method has a better cloaking effect on the incident wave along the ellipse minor axis direction than the traditional method. This means that for the same object, an appropriate transformation scheme can be selected for different incident wave directions to achieve the optimal control effect. The validated scheme is further used to design an arch-shaped cloak composed of an upper semicircular area and a lower rectangular area, by combining the traditional single-centered coordinate transformation method for the semicircular area and the proposed multi-origin method for the rectangular area. The results show that the designed cloak can effectively control the wave propagation with significantly reduced acoustic pressure level. This work provides a flexible acoustic cloak design method applicable for arbitrary shapes and different wave incident directions, enriching the theory of acoustic cloaking based on coordinate transformation.