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As a newly-developed method, acoustic cloak made of pentamode materials is on its speedway to the promising potential application. However, physical fabrication of pentamode cloak with continuously varying material parameters can be a tough work, if not totally impossible. Layering is a natural compromise to bypass this quandary. Researches on layering effects of inertial cloak are ample. However, researches on layering pentamode acoustic cloak are relatively limited. Among these researches Scandrett extends the effective bandwidth through optimization of material parameters[2010 J. Acoust. Soc. Am. 127 2856, 2011 Wave Motion. 48 505].#br#The present work concerns the layering effects of pentamode acoustic cloak. By comparing with precedent results, the present paper has two major innovations: Firstly, cylinder is chosen to be the basic geometry. This is of obvious advantage since cylinder is the basic geometry of acoustic cloak's important potential host. Secondly, effects of layers' number and thickness distribution on the stealth effect are analyzed. The two are key parameters to be determined in the layering process. This paper is organized as follows: Firstly, analytical expression of the scattering pressure field of layered cloak is deduced by means of variables separation. In this process Fourier expansion plays a key role. And the harmonic assumption of the incident acoustic wave is made. Secondly, typical cases are calculated to verify the validation of the theoretical analysis. First let material parameters tend towards that of water, and compare the scattering field with that of the bare rigid object when the cloak is replaced by water. Second let the layering number goes to infinity, and compare the scattering field with that of the continuous cloak. Phenomena conforming with basic physical laws are observed. And validity of the theory and codes is confirmed. Thirdly, effects of layers' number and thickness distribution on the stealth character are theoretically and numerically analyzed. One can easily see from the computational results that a critical number N exists. When layers' number exceeds N, improvement of the stealth effect becomes less efficient by further adding layers' number. One can also see from the computational results that a wise distributional strategy that helps improve the stealth effect indeed exists. And the optimization iteration can be utilized to further improve it.#br#As a summary, the present paper concerns the layering process of cloaking. Qualitatively and quantitatively, several significant results are obtained. This paper offers a useful reference for future fabrication of realistic acoustic pentamode cloak.
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Keywords:
- acoustic cloak /
- pentamode material /
- layering
[1] Leonhardt U 2006 Science 312 1777
[2] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[3] Kwon D H, Werner D H 2008 Appl. Phys. Lett. 92 013505
[4] Schurig D, Mock J J, Justice B J, Cummer S A, Pendry J B, Starr A F, Smith D R 2006 Science 314 977
[5] Ma H, Qu S B, Xu Z, Zhang J Q, Wang J F 2009 Chin. Phys. B 18 1025
[6] Wu Q, Zhang K, Meng FY, Li LW 2009 Acta Phys. Sin. 58 1619 (in Chinese) [吴群, 张狂, 孟繁义, 李乐伟 2009 物理学报 58 1619]
[7] Guo P F, Li D, Dai Q, Fu Y Q 2013 Chin. Phys. B 22 054101
[8] Smolyaninov I I, Smolyaninova V N, Kildishev A V, Shalaev V M 2009 Phys. Rev. Lett. 102 213901
[9] Cummer S A, Popa B I, Schurig D, Smith D R, Pendry J B 2006 Phys. Rev. E 74 036621
[10] Ruan Z, Yan M, Neff C W, Qiu M 2007 Phys. Rev. Lett. 99 113903
[11] Luo XY, Liu DY, Yao LF, Dong JF 2014 Acta Phys. Sin. 63 084101 (in Chinese) [罗孝阳, 刘道亚, 姚丽芳, 董建峰 2014 物理学报 63 084101]
[12] Cummer S A, Schurig D 2007 New J. Phys. 9 45
[13] Chen H, Chan C T 2007 Appl. Phys. Lett. 91 183518
[14] Cummer S A, Popa B I, Schurig D, Smith D R, Pendry J B, Rahm M, Starr A 2008 Phys. Rev. Lett. 100 024301
[15] Cummer S A, Rahm M, Schurig D 2008 New J. Phys. 10 115025
[16] Liang W C, Sánchez-Dehesa J 2007 J. Phys. 9 010450
[17] Torrent D, Sánchez-Dehesa J 2008 New J. Phys. 10 063015
[18] Farhat M, Guenneau S, Enoch S, Movchan A, Zolla F, Nicolet A 2008 New J. Phys. 10 115030
[19] Norris A N 2008 Proc. R. Soc. A 464 2411
[20] Hu J, Liu X N, Hu G K 2013 Wave Motion 170
[21] Layman C J, Naify C J, Martin T P, Calvo D C, Orris G J 2013 Phys. Rev. Lett. 111 024302
[22] Bckmann T, Thiel M, Kadic1 M, Schittny R, Wegener M 2014 Nature Communications 5 4130
[23] 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]
[24] Cai L, Wen J H, Yu D L, Lu Z M, Wen X S 2014 Chin. Phys. Lett. 31 094303
[25] Scandrett C L, Boisvert J E, Howarth T R 2010 J. Acoust. Soc. Am. 127 2856
[26] Scandrett C L, Boisvert J E, Howarth T R 2011 Wave Motion. 48 505
[27] Du G H, Zhu Z M, Gong X F 2012 Basic Acoustics (Nanjing: Nanjing University Press) (in Chinese) [杜功焕, 朱哲民, 龚秀芬 2012 声学基础(南京: 南京大学出版社)]
[28] Jones D S 1986 Acoustic and Electromagnetic Waves (Oxford: Clarendon Press)
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[1] Leonhardt U 2006 Science 312 1777
[2] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[3] Kwon D H, Werner D H 2008 Appl. Phys. Lett. 92 013505
[4] Schurig D, Mock J J, Justice B J, Cummer S A, Pendry J B, Starr A F, Smith D R 2006 Science 314 977
[5] Ma H, Qu S B, Xu Z, Zhang J Q, Wang J F 2009 Chin. Phys. B 18 1025
[6] Wu Q, Zhang K, Meng FY, Li LW 2009 Acta Phys. Sin. 58 1619 (in Chinese) [吴群, 张狂, 孟繁义, 李乐伟 2009 物理学报 58 1619]
[7] Guo P F, Li D, Dai Q, Fu Y Q 2013 Chin. Phys. B 22 054101
[8] Smolyaninov I I, Smolyaninova V N, Kildishev A V, Shalaev V M 2009 Phys. Rev. Lett. 102 213901
[9] Cummer S A, Popa B I, Schurig D, Smith D R, Pendry J B 2006 Phys. Rev. E 74 036621
[10] Ruan Z, Yan M, Neff C W, Qiu M 2007 Phys. Rev. Lett. 99 113903
[11] Luo XY, Liu DY, Yao LF, Dong JF 2014 Acta Phys. Sin. 63 084101 (in Chinese) [罗孝阳, 刘道亚, 姚丽芳, 董建峰 2014 物理学报 63 084101]
[12] Cummer S A, Schurig D 2007 New J. Phys. 9 45
[13] Chen H, Chan C T 2007 Appl. Phys. Lett. 91 183518
[14] Cummer S A, Popa B I, Schurig D, Smith D R, Pendry J B, Rahm M, Starr A 2008 Phys. Rev. Lett. 100 024301
[15] Cummer S A, Rahm M, Schurig D 2008 New J. Phys. 10 115025
[16] Liang W C, Sánchez-Dehesa J 2007 J. Phys. 9 010450
[17] Torrent D, Sánchez-Dehesa J 2008 New J. Phys. 10 063015
[18] Farhat M, Guenneau S, Enoch S, Movchan A, Zolla F, Nicolet A 2008 New J. Phys. 10 115030
[19] Norris A N 2008 Proc. R. Soc. A 464 2411
[20] Hu J, Liu X N, Hu G K 2013 Wave Motion 170
[21] Layman C J, Naify C J, Martin T P, Calvo D C, Orris G J 2013 Phys. Rev. Lett. 111 024302
[22] Bckmann T, Thiel M, Kadic1 M, Schittny R, Wegener M 2014 Nature Communications 5 4130
[23] 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]
[24] Cai L, Wen J H, Yu D L, Lu Z M, Wen X S 2014 Chin. Phys. Lett. 31 094303
[25] Scandrett C L, Boisvert J E, Howarth T R 2010 J. Acoust. Soc. Am. 127 2856
[26] Scandrett C L, Boisvert J E, Howarth T R 2011 Wave Motion. 48 505
[27] Du G H, Zhu Z M, Gong X F 2012 Basic Acoustics (Nanjing: Nanjing University Press) (in Chinese) [杜功焕, 朱哲民, 龚秀芬 2012 声学基础(南京: 南京大学出版社)]
[28] Jones D S 1986 Acoustic and Electromagnetic Waves (Oxford: Clarendon Press)
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