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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.
[1] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[2] Milton G W, Briane M, Willis J R 2006 New J. Phys. 8 248
[3] Chen H Y, Chan C T 2010 J. Phys. D: Appl. Phys. 43 113001
[4] Cummer S A, Schurig D 2007 New J. Phys. 9 45
[5] Norris A N 2008 Proc. R. Soc. 464 2411
[6] Tian H W 2013 M. S. Thesis (Changsha: National University of Defense Technology) (in Chinese) [田华文 2007 硕士学位论文(长沙: 国防科技大学)]
[7] Maldovan M 2013 Nature 503 209
[8] Gao D B, Zeng X W 2012 Acta Phys. Sin. 61 184301 (in Chinese) [高东宝, 曾新吾 2012 物理学报 61 184301]
[9] Hu J, Zhou X M, Hu G K 2009 ASME 2009 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineerings, USA
[10] Shen H J, Wen J H, Yu D L, Cai L, Wen X S 2012 Acta Phys. Sin. 61 134303 (in Chinese) [沈惠杰, 温激鸿, 郁殿龙, 蔡力, 温熙森 2012 物理学报 61 134303]
[11] Torrent D, Snchez-Dehesa J 2008 New J. Phys. 10 063015
[12] Zhang S, Xia C G, Fang N 2011 Phys Rev. Lett. 106 024301
[13] Sanchis L, Garcia-chocano V M, Liopis-Pontivero S R 2013 Phys. Rev. Lett. 110 124301
[14] Cheng Y, Liu X J 2009 Appl. Phys. A 94 25
[15] Norris A N, Nagy J A 2010 J. Acoust. Soc. Am. 120 1606
[16] Norris A N, Nagy J A 2011 Phononics 2011: First International Conference on Phononic Crystals, Metamaterials and Optomechanics Santa Fe, New Mexico, USA, May 29-June 2, 2011 p112
[17] Milton G W, Cherkaev A V 1995 J. Eng. Mater. Technol. 117 483
[18] Hladky-Hennion C A, Vasseur O J, Haw G, Croenne C, Haumesser L, Norris N A 2013 Appl Phys. Lett. 102 14413
[19] Layman N C, Naify J C, Martin P T, Calvo C D, Orris J G 2012 Phys. Rev. Lett. 111 024302
[20] Martin A, Kadic M, Schittny R, Buckmann T, Wegener M 2012 Phys. Rev. B 86 155116
[21] Nagy A J 2015 Ph. D. Dissertation (New Jersey: Rutgers University)
[22] Yi H, Wang X M, Mei Y L 2015 Chin. J. Sol. Mech. 36 4 (in Chinese) [易辉, 王晓明, 梅玉林 2015 固体力学学报 36 4]
[23] Cai C X, Wang Z H, Li Q W, Xu Z, Tian X G 2015 J. Phys. D: Appl. Phys. 48 175103
[24] Kadic M, Bukmann T, Schittny R, Gumbsch P, Wegener M 2014 Phys. Rev. A 2 054007
[25] Zhang Y L 2014 M. S. Thesis (Dalian: Dalian University of Technology) (in Chinese) [张迎龙 2014 硕士学位论文(大连: 大连理工大学)]
[26] Bckmann T, Kadic M, Schittny R, Wegener M 2015 Proc. Natl. Acad. Sci. 16 112
[27] Huang Y, Lu X G, Liang G Y, Xu Z 2016 Phys. Lett. A 380 1334
[28] Scandrett L C, Boisvert E J, Howarth R T 2010 J. Acoust. Soc. Am. 127 2856
[29] Tian Y, Wei Q, Cheng Y, Xu Z, Liu X J 2015 Appl. Phys. Lett. 107 221906
[30] Chen Y, Liu X N, Hu G K 2015 Sci. Rep. 5 15745
[31] Chen Y, Liu X N, Xiang P, Hu G K 2016 Advances in Mechanics 46 201609 (in Chinese) [陈毅, 刘晓宁, 向平, 胡更开 2016 力学进展 46 201609]
[32] Zhang X D, Chen H, Wang L, Zhao Z G, Zhao A G 2015 Acta Phys. Sin. 64 134303 (in Chinese) [张向东, 陈虹, 王磊, 赵志高, 赵爱国 2015 物理学报 64 134303]
[33] Gokhale H N, Cipolla L J, Norris N A 2012 Special Issue of J. Acoustic. Soc. Am. 127 2856
[34] Cheng Y, Yang F, Xu J Y, Liu X J 2008 Appl. Phys. Lett. 92 151913
[35] Cheng Y, Liu X J 2008 J. Appl. Phys. 104 104911
[36] Torrent D, Snchez-Dehesa J 2011 Wave Motion 6 48
[37] Cai L W, Snchez-Dehesa J 2012 J. Acoust. Soc. Am. 4 132
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[1] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[2] Milton G W, Briane M, Willis J R 2006 New J. Phys. 8 248
[3] Chen H Y, Chan C T 2010 J. Phys. D: Appl. Phys. 43 113001
[4] Cummer S A, Schurig D 2007 New J. Phys. 9 45
[5] Norris A N 2008 Proc. R. Soc. 464 2411
[6] Tian H W 2013 M. S. Thesis (Changsha: National University of Defense Technology) (in Chinese) [田华文 2007 硕士学位论文(长沙: 国防科技大学)]
[7] Maldovan M 2013 Nature 503 209
[8] Gao D B, Zeng X W 2012 Acta Phys. Sin. 61 184301 (in Chinese) [高东宝, 曾新吾 2012 物理学报 61 184301]
[9] Hu J, Zhou X M, Hu G K 2009 ASME 2009 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineerings, USA
[10] Shen H J, Wen J H, Yu D L, Cai L, Wen X S 2012 Acta Phys. Sin. 61 134303 (in Chinese) [沈惠杰, 温激鸿, 郁殿龙, 蔡力, 温熙森 2012 物理学报 61 134303]
[11] Torrent D, Snchez-Dehesa J 2008 New J. Phys. 10 063015
[12] Zhang S, Xia C G, Fang N 2011 Phys Rev. Lett. 106 024301
[13] Sanchis L, Garcia-chocano V M, Liopis-Pontivero S R 2013 Phys. Rev. Lett. 110 124301
[14] Cheng Y, Liu X J 2009 Appl. Phys. A 94 25
[15] Norris A N, Nagy J A 2010 J. Acoust. Soc. Am. 120 1606
[16] Norris A N, Nagy J A 2011 Phononics 2011: First International Conference on Phononic Crystals, Metamaterials and Optomechanics Santa Fe, New Mexico, USA, May 29-June 2, 2011 p112
[17] Milton G W, Cherkaev A V 1995 J. Eng. Mater. Technol. 117 483
[18] Hladky-Hennion C A, Vasseur O J, Haw G, Croenne C, Haumesser L, Norris N A 2013 Appl Phys. Lett. 102 14413
[19] Layman N C, Naify J C, Martin P T, Calvo C D, Orris J G 2012 Phys. Rev. Lett. 111 024302
[20] Martin A, Kadic M, Schittny R, Buckmann T, Wegener M 2012 Phys. Rev. B 86 155116
[21] Nagy A J 2015 Ph. D. Dissertation (New Jersey: Rutgers University)
[22] Yi H, Wang X M, Mei Y L 2015 Chin. J. Sol. Mech. 36 4 (in Chinese) [易辉, 王晓明, 梅玉林 2015 固体力学学报 36 4]
[23] Cai C X, Wang Z H, Li Q W, Xu Z, Tian X G 2015 J. Phys. D: Appl. Phys. 48 175103
[24] Kadic M, Bukmann T, Schittny R, Gumbsch P, Wegener M 2014 Phys. Rev. A 2 054007
[25] Zhang Y L 2014 M. S. Thesis (Dalian: Dalian University of Technology) (in Chinese) [张迎龙 2014 硕士学位论文(大连: 大连理工大学)]
[26] Bckmann T, Kadic M, Schittny R, Wegener M 2015 Proc. Natl. Acad. Sci. 16 112
[27] Huang Y, Lu X G, Liang G Y, Xu Z 2016 Phys. Lett. A 380 1334
[28] Scandrett L C, Boisvert E J, Howarth R T 2010 J. Acoust. Soc. Am. 127 2856
[29] Tian Y, Wei Q, Cheng Y, Xu Z, Liu X J 2015 Appl. Phys. Lett. 107 221906
[30] Chen Y, Liu X N, Hu G K 2015 Sci. Rep. 5 15745
[31] Chen Y, Liu X N, Xiang P, Hu G K 2016 Advances in Mechanics 46 201609 (in Chinese) [陈毅, 刘晓宁, 向平, 胡更开 2016 力学进展 46 201609]
[32] Zhang X D, Chen H, Wang L, Zhao Z G, Zhao A G 2015 Acta Phys. Sin. 64 134303 (in Chinese) [张向东, 陈虹, 王磊, 赵志高, 赵爱国 2015 物理学报 64 134303]
[33] Gokhale H N, Cipolla L J, Norris N A 2012 Special Issue of J. Acoustic. Soc. Am. 127 2856
[34] Cheng Y, Yang F, Xu J Y, Liu X J 2008 Appl. Phys. Lett. 92 151913
[35] Cheng Y, Liu X J 2008 J. Appl. Phys. 104 104911
[36] Torrent D, Snchez-Dehesa J 2011 Wave Motion 6 48
[37] Cai L W, Snchez-Dehesa J 2012 J. Acoust. Soc. Am. 4 132
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