Acoustic Metamaterial Design Method Based on Green Coordinate Transformation

Abstract:

Acoustic metamaterials have great application prospects in eliminating vibration and noise, but they are difficult to manufacture due to their anisotropy. This paper utilizes the Green coordinate transformation method to design acoustic metamaterials by combining with the transformation acoustics theory. Because the Green coordinate transformation is the pseudo-conformal mapping in three-dimensional coordinates, the anisotropy of designed metamaterials can be weakened. And also, the genetic algorithm is employed to optimize the anisotropy of metamaterials and reduce the designed metamaterial parameter difference further. Finally, the membrane-imbedded-type metamaterial is applied to realize the design and to illustrate the effectiveness of the proposed method by manipulating the acoustic wave propagation path.

• Periodical: Materials Science Forum (Volume 976)
• Pages: 15-24
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.976.15
• Online since: January 2020
• Authors: Xin Xie, Xiao Ming Wang, Yu Lin Mei*
• Keywords: Acoustic Metamaterials, Genetic Algorithm, Green Coordinate Transformation, Transformation Acoustics, Wave Propagation

References

[1] Wu Jiuhui, Ma Fuyin, Zhang Siwen. Application of Acoustic Metamaterials in Low-frequency Vibration and Noise Reduction [J]. Journal of Mechanical Engineering, 2016, 52(13): 68-78.

DOI: 10.3901/jme.2016.13.068

[2] J. B. Pendry, D. Schurig and D. R. Smith. Controlling Electromagnetic Fields [J]. Science, 2006, 312(5781): 1780-1782.

DOI: 10.1126/science.1125907

[3] Leonhardt U. Optics Conformal Mapping [J]. Science, 2006, 312(5781): 1777-1780.

DOI: 10.1126/science.1126493

[4] S. A. Cummer and D. Schurig. One Path to Acoustic Cloaking [J]. New J. Phys., 2007, 9: 45.

DOI: 10.1088/1367-2630/9/3/045

[5] V.G. Veselago. The Electrodynamics of Substances with Simultaneously Negative Values of and [J]. Soviet Physics Uspekhi, 1968, 10(4): 509-514.

DOI: 10.1070/pu1968v010n04abeh003699

[6] J. B. Pendry, A. J. Holden, W. J. Stewart and I. Youngs. Extremely Low Frequency Plasmons in Metallic Mesostructures [J]. Physical Review Letters, 1996, 76(25): 4773-4776.

DOI: 10.1103/physrevlett.76.4773

[7] J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart. Magnetism from Conductors and Enhanced Nonlinear Phenomena [J]. IEEE Transactions on Microwave Theory and Techniques, 1999, 47(11): 2075-2084.

DOI: 10.1109/22.798002

[8] Gao Dongbao, Zeng Xinwu. Layered Elliptical-cylindrical Acoustic Cloaking Design Based on Isotropic Materials [J]. Acta Physica Sinica, 2012, 61(18): 260-267.

DOI: 10.7498/aps.61.184301

[9] Shen Huijie, Wen Jihong, Yu Dianlong, Cai Li, Wen Xisen. Research on a Cylindrical Cloak with Active Acoustic Metamaterial Layers [J]. Acta Physica Sinica, 2012, 61(13): 230-237.

DOI: 10.7498/aps.61.134303

[10] Zhang S, Yin L, Fang N. Focusing Ultrasound with an Acoustic Metamaterial Network [J]. Physical Review Letters, 2009, 102(19): 194301.

DOI: 10.1103/physrevlett.102.194301

[11] Li Y, Liang B, Tao X. Acoustic Focusing by Coiling up Space [J]. Applied Physics Letters, 2012, 101(23): 036609.

[12] Y. Lipman, D. Levin. Derivation and Analysis of Green Coordinates [J]. Computational Methods & Function Theory, 2010, 10(1): 167-188.

DOI: 10.1007/bf03321761

[13] A. N. Norris. Acoustic Cloaking Theory [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2008, 464(2097): 2411-2434.

DOI: 10.1098/rspa.2008.0076

[14] Y. Li, X. M. Wang, Y. L. Mei*. Acoustic Characteristics of 3-D Membrane-embedded-type Metamaterials, Proceedings of the International Conference on Computational Methods (ICCM2017) 2017, Guilin, Guangxi, China, 914-925.