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In this paper, by taking the acoustic property of a two-dimensional squarely arranged Helmholtz resonator array for example, we point out that there exist two kinds of couplings in the local resonance phononic crystal, which are the coupling between the resonator and background and the coupling among the resonators, respectively. The first coupling effect can be changed by changing the quality factor of the resonator. A local-resonant type of band gap can be converted into a Bragg-scattering type continually when this kind of coupling becomes larger and larger. The second one, which is based on the overlapping of the near filed around the resonators, can be enhanced by reducing the distance between the nearest resonators. As a result, a wider band gap, but a smaller penetration depth of the wave, can be obtained.
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Keywords:
- local resonance /
- acoustic band gap /
- Helmholtz resonator
[1] Kuang W M, Hou Z L, Liu Y Y 2004 Phys. Lett. A 332 481
[2] Gao G Y, Ma S L, Jin F, Jin D F, Lu T J 2010 Acta Phys. Sin. 59 393 (in Chinese) [高国钦, 马守林, 金峰, 金东范, 卢天健 2010 物理学报 59 393]
[3] Hao G J, Fu X J, Hou Z L 2009 Acta Phys. Sin. 58 8484 (in Chinese) [郝国郡, 付秀军, 侯志林 2009 物理学报 58 8484]
[4] Sigalas M M, Economou E N 1994 J. Appl. Phys. 75 2845
[5] Kafesaki M, Sigalas M M, Economou E N 1995 Solid State Common. 96 285
[6] Oudich M, Li Y, Assouar B M, Hou Z L 2010 New J. Phys. 12 083049
[7] Liu Z Y, Chan C T, Sheng P 2002 Phys. Rev. B 65 165116
[8] Wang G, Wen X S, Wen J H, Shao L H, Liu Y Z 2004 Phys. Rev. Lett. 93 154302
[9] Liu Z Y, Zhang X X, Mao Y W, Zhu Y Y, Yang Z Y, Chan C T, Sheng P 2000 Science 289 1734
[10] Mei J, Liu Z Y, Wen W J, Sheng P 2008 Phys. Rev. B 76 134205
[11] Fang N, Xi D J, Xu J Y, Ambati M, Srituravanich W, Sun C, Zhang X 2006 Nature Materials 5 452
[12] Cheng Y, Xu J Y, Lin X J 2008 Phys. Rev. B 77 045143
[13] Cheng Y, Xu J Y, Lin X J 2008 Appl. Phys. Lett. 92 051913
[14] Fok L, Zhang X 2011 Phys .Rev. B 83 214304
[15] Goffaux C, Sanchez-Dehesa J, Levy Y A, Lambin P, Khelif A, Vasseur J O, Rouhani-Djafari B 2002 Phys. Rev. Lett. 88 225502
[16] Hu X H, Chan C T, Zi J 2005 Phys. Rev. E 71 055601
[17] Hou Z L, Liu J T, Kuang W M, Liu Y Y, Wu S Z 2007 Phys. Rev. E 75 026608
[18] Morse P M 1974 Vibration and Sound (1st) p31 (in Chinese) [南京大学翻译组 译 1974 振动与声 (第一版)(北京:科学出版社) 第31页]
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[1] Kuang W M, Hou Z L, Liu Y Y 2004 Phys. Lett. A 332 481
[2] Gao G Y, Ma S L, Jin F, Jin D F, Lu T J 2010 Acta Phys. Sin. 59 393 (in Chinese) [高国钦, 马守林, 金峰, 金东范, 卢天健 2010 物理学报 59 393]
[3] Hao G J, Fu X J, Hou Z L 2009 Acta Phys. Sin. 58 8484 (in Chinese) [郝国郡, 付秀军, 侯志林 2009 物理学报 58 8484]
[4] Sigalas M M, Economou E N 1994 J. Appl. Phys. 75 2845
[5] Kafesaki M, Sigalas M M, Economou E N 1995 Solid State Common. 96 285
[6] Oudich M, Li Y, Assouar B M, Hou Z L 2010 New J. Phys. 12 083049
[7] Liu Z Y, Chan C T, Sheng P 2002 Phys. Rev. B 65 165116
[8] Wang G, Wen X S, Wen J H, Shao L H, Liu Y Z 2004 Phys. Rev. Lett. 93 154302
[9] Liu Z Y, Zhang X X, Mao Y W, Zhu Y Y, Yang Z Y, Chan C T, Sheng P 2000 Science 289 1734
[10] Mei J, Liu Z Y, Wen W J, Sheng P 2008 Phys. Rev. B 76 134205
[11] Fang N, Xi D J, Xu J Y, Ambati M, Srituravanich W, Sun C, Zhang X 2006 Nature Materials 5 452
[12] Cheng Y, Xu J Y, Lin X J 2008 Phys. Rev. B 77 045143
[13] Cheng Y, Xu J Y, Lin X J 2008 Appl. Phys. Lett. 92 051913
[14] Fok L, Zhang X 2011 Phys .Rev. B 83 214304
[15] Goffaux C, Sanchez-Dehesa J, Levy Y A, Lambin P, Khelif A, Vasseur J O, Rouhani-Djafari B 2002 Phys. Rev. Lett. 88 225502
[16] Hu X H, Chan C T, Zi J 2005 Phys. Rev. E 71 055601
[17] Hou Z L, Liu J T, Kuang W M, Liu Y Y, Wu S Z 2007 Phys. Rev. E 75 026608
[18] Morse P M 1974 Vibration and Sound (1st) p31 (in Chinese) [南京大学翻译组 译 1974 振动与声 (第一版)(北京:科学出版社) 第31页]
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