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

doi:10.1007/s10483-022-2928-7

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (11): 1641-1656.doi: https://doi.org/10.1007/s10483-022-2928-7

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

Pengfei LI¹, Fan YANG¹, Peng WANG¹, Jinfeng ZHAO¹, Zheng ZHONG^1,2

1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China;
2. School of Science, Harbin Institute of Technology, Shenzhen 518055, Guangdong Province, China

收稿日期:2022-07-08 修回日期:2022-09-04 发布日期:2022-10-29
通讯作者: Fan YANG, E-mail: fanyang@tongji.edu.cn; Zheng ZHONG, E-mail: zhongk@tongji.edu.cn
基金资助:
This work is supported by the opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (No. KFJJ22-08M), the State Key Laboratory of Mechanics and Control of Mechanical Structures (No. MCMS-E-0221G02), and Shanghai Supercomputer Center.

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

Pengfei LI¹, Fan YANG¹, Peng WANG¹, Jinfeng ZHAO¹, Zheng ZHONG^1,2

1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China;
2. School of Science, Harbin Institute of Technology, Shenzhen 518055, Guangdong Province, China

Received:2022-07-08 Revised:2022-09-04 Published:2022-10-29
Contact: Fan YANG, E-mail: fanyang@tongji.edu.cn; Zheng ZHONG, E-mail: zhongk@tongji.edu.cn
Supported by:
This work is supported by the opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (No. KFJJ22-08M), the State Key Laboratory of Mechanics and Control of Mechanical Structures (No. MCMS-E-0221G02), and Shanghai Supercomputer Center.

摘要/Abstract

摘要： 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.

关键词: metamaterial, acoustic cloak, transformation acoustic, region partitioning, finite element (FE) simulation

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.

Key words: metamaterial, acoustic cloak, transformation acoustic, region partitioning, finite element (FE) simulation

中图分类号:

74H45

Pengfei LI, Fan YANG, Peng WANG, Jinfeng ZHAO, Zheng ZHONG. A novel design scheme for acoustic cloaking of complex shape based on region partitioning and multi-origin coordinate transformation[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(11): 1641-1656.

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

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

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