Please wait a minute...
Chin. Phys. B, 2015, Vol. 24(2): 024303    DOI: 10.1088/1674-1056/24/2/024303
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Homogenization theory for designing graded viscoelastic sonic crystals

Qu Zhao-Liang (曲兆亮), Ren Chun-Yu (任春雨), Pei Yong-Mao (裴永茂), Fang Dai-Ning (方岱宁)
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
Abstract  In this paper, we propose a homogenization theory for designing graded viscoelastic sonic crystals (VSCs) which consist of periodic arrays of elastic scatterers embedded in a viscoelastic host material. We extend an elastic homogenization theory to VSC by using the elastic-viscoelastic correspondence principle and propose an analytical effective loss factor of VSC. The results of VSC and the equivalent structure calculated by using the finite element method are in good agreement. According to the relation of the effective loss factor to the filling fraction, a graded VSC plate is easily and quickly designed. Then, the graded VSC may have potential applications in the vibration absorption and noise reduction fields.
Keywords:  graded sonic crystals      homogenization theory      viscoelasticity  
Received:  18 May 2014      Revised:  22 August 2014      Accepted manuscript online: 
PACS:  43.35.Gk (Phonons in crystal lattices, quantum acoustics)  
  83.60.Bc (Linear viscoelasticity)  
Fund: Project supported by the National Basic Research Program of China (Grant No. 2011CB610301).
Corresponding Authors:  Pei Yong-Mao, Fang Dai-Ning     E-mail:  peiym@pku.edu.cn;fangdn@pku.edu.cn

Cite this article: 

Qu Zhao-Liang (曲兆亮), Ren Chun-Yu (任春雨), Pei Yong-Mao (裴永茂), Fang Dai-Ning (方岱宁) Homogenization theory for designing graded viscoelastic sonic crystals 2015 Chin. Phys. B 24 024303

[1] Kushwaha M S, Halevi P, Dobrzynski L and Djafari-Rouhani B 1993 Phys. Rev. Lett. 71 2022
[2] Vasseur J O, Deymier P A, Chenni B, Djafari-Rouhani B, Dobrzynski L and Prevost D 2001 Phys. Rev. Lett. 86 3012
[3] Gao D B, Zeng X W, Zhou Z M and Tian Z F 2013 Acta Phys. Sin. 62 094304 (in Chinese)
[4] Wei Q, Cheng Y and Liu X J 2011 Acta Phys. Sin. 60 124301 (in Chinese)
[5] Xu Y L, Tian X G and Chen C Q 2012 Physica B 407 1995
[6] Alagoz S 2012 Chin. Phys. B 21 126202
[7] Yang S X, Page J H, Liu Z Y, Cowan M L, Chan C T and Sheng P 2004 Phys. Rev. Lett. 93 024301
[8] Alagoz S and Alagoz B B 2013 Chin. Phys. B 22 076201
[9] Fan L, Zhang S Y and Zhang H 2011 Chin. Phys. Lett. 28 104301
[10] Liu C, Xu X D and Liu X J 2013 Acta Phys. Sin. 62 204302 (in Chinese)
[11] Atak O, Huybrechs D, Pluymers B and Desmet W 2014 J. Sound Vib. 333 3367
[12] Merheb B, Deymier P A, Jain M, Aloshyna-Lesuffleur M, Mohanty S, Berker A and Greger R W 2008 J. Appl. Phys. 104 064913
[13] Merheb B, Deymier P A, Muralidharan K, Bucay J, Jain M, Aloshyna-Lesuffleur M, Greger R W, Mohanty S and Berker A 2009 Modelling Simul. Mater. Sci. Eng. 17 075013
[14] Psarobas I E 2001 Phys. Rev. B 64 012303
[15] Zhao Y P and Wei P J 2009 Comput. Mater. Sci. 46 603
[16] Wei P J and Zhao Y P 2010 Mech. Adv. Mater. Struc. 17 383
[17] Wu L Y and Chen L W 2011 J. Appl. Phys. 110 114507
[18] Lin S C S, Huang T J, Sun J H and Wu T T 2009 Phys. Rev. B 79 094302
[19] Lin S C S, Bernhard R T, Sun J H, Wu T T and Huang T J 2009 J. Phys. D: Appl. Phys. 42 185502
[20] Deng Ke, Ding Y Q, He Z J, Zhao H P, Shi J and Liu Z Y 2009 J. Phys. D: Appl. Phys. 42 185505
[21] Theodore P M, Michael N, Gregory J O, Cai L W, Daniel T and José Sánchez-Dehesa 2010 Appl. Phys. Lett. 97 113503
[22] Peng S S, He Z J, Jia H, Zhang A Q, Qiu C Y, Ke M Z and Liu Z Y 2010 Appl. Phys. Lett. 96 263502
[23] Hou Z L, Wu F G, Fu X J and Liu Y Y 2005 Phys. Rev. E 71 037604
[24] Daniel T and José Sánchez-Dehesa 2006 Phys. Rev. B 74 224305
[25] Ni Q and Cheng J C 2005 Chin. Phys. Lett. 22 2305
[26] Liu Y H, Chang C C, Chern R L and Chang C C 2007 Phys. Rev. B 75 054104
[27] Krokhin A A, Arriaga J and Gumen L N 2003 Phys. Rev. Lett. 91 264302
[1] Hybrid natural element method for viscoelasticity problems
Zhou Yan-Kai (周延凯), Ma Yong-Qi (马永其), Dong Yi (董轶), Feng Wei (冯伟). Chin. Phys. B, 2015, 24(1): 010204.
[2] A dynamic rheological model for thin-film lubrication
Zhang Xiang-Jun (张向军), Huang Ying (黄颖), Guo Yan-Bao (郭岩宝), Tian Yu (田煜), Meng Yong-Gang (孟永钢). Chin. Phys. B, 2013, 22(1): 016202.
[3] Complex variable element-free Galerkin method for viscoelasticity problems
Cheng Yu-Min (程玉民), Li Rong-Xin (李荣鑫), Peng Miao-Juan (彭妙娟). Chin. Phys. B, 2012, 21(9): 090205.
[4] The viscoelasticity of lipid shell and the hysteresis of subharmonic in liquid containing microbubbles
Gong Yan-Jun (龚燕君), Zhang Dong (章东), Gong Xiu-Fen (龚秀芬), Tan Kai-Bin (谭开彬), Liu Zheng (刘政). Chin. Phys. B, 2006, 15(7): 1526-1531.
No Suggested Reading articles found!