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本文提出了一种新型局域共振复合单元声子晶体结构, 并结合有限元方法对结构的带隙机理及低频共振带隙特性进行了分析和研究. 共振带隙产生的频率位置由所对应的局域共振模态的固有频率决定, 并且带隙宽度与局域共振模态的品质因子及其与基体之间的耦合作用强度有关. 采用局域共振复合单元结构可以实现声子晶体的多重共振, 在低频范围能打开多条共振带隙, 但受到共振单元排列方式的的影响. 由于纵向和横向局域共振模态的简并, 复合单元结构能在200 Hz以下的低频范围打开超过60%宽度的共振带隙, 最低带隙频率低至18 Hz. 这为声子晶体结构获得低频、超低频带隙提供了一种有效的方法.In this paper, a novel locally resonant structure with composite units is proposed. Formation mechanisms and low-frequency characteristics of the band gaps in the proposed structure are investigated using finite element methods. Frequency positions of band gaps depend on natural frequencies of the corresponding locally resonant modes. And the gap width is related to both the Q factor of the locally resonant modes and the interaction strength in-between the locally resonant structural units. Phononic crystal structures with composite units exhibit multiple resonances and band gaps in low-frequency range, depending on the arrangement of locally resonant units. Due to the mode degeneracy of the vertical and horizontal local resonances, the composite structures possess band gaps below 200Hz with the total gap width more than 60% and the lowest frequency down to 18Hz. The structures and results provide a new effective method for phononic crystal structures to obtain broadband gaps in low-frequency range.
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Keywords:
- localized resonance /
- low frequency band gaps /
- composite units /
- phononic crystals
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[1] Roundy S 2005 J. Intell. Mater. Syst. Struct. 16 809
[2] Liu B, Feng T, Wu X, Huang Z G, Zhu T F 2010 Noise and Vibration Control 3 50 (in Chinese) [刘斌, 冯涛, 吴雪, 黄志刚, 朱腾飞 2010 噪声与振动控制 3 50]
[3] Tempest W 1976 Infrasound and Low Frequency Vibration (London: Academic Press Inc.) p187
[4] Wen X S, Wen J H, Yu D L, Wang G, Liu Y Z, Han X Y 2009 Phononic Crystals (Beijing: National Defense Industry Press) p2 (in Chinese) [温熙森, 温激鸿, 郁殿龙, 王刚, 刘耀宗, 韩小云 2009 声子晶体 (北京: 国防工业出版社) 第2页]
[5] Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, Sheng P 2000 Science 289 5485
[6] Liu Z, Chan C T, Sheng P 2002 Phys. Rev. B 65 165116
[7] Wang G, Shao L H, Liu Y Z, Wen J H 2006 Chin. Phys. 15 1843
[8] Ho K M, Cheng K, Yang Z, Zhang X X, Sheng P 2003 Appl. Phys. Lett. 83 5566
[9] Yu D, Liu Y, Wang G, Cai L, Qiu J 2006 Phys. Lett. A 348 410
[10] Wen Q H, Zuo S G, Wei H 2012 Acta Phys. Sin. 61 034301 (in Chinese) [文岐华, 左曙光, 魏欢 2012 61 034301]
[11] Pennec Y, Djafari-Rouhani B, Larabi H, Vasseur J O, Hladky-Hennion A C 2008 Phys. Rev. B 78 104105
[12] Oudich M, Li Y, Assouar B M, Hou Z L 2010 New J. Phys. 12 083049
[13] Hsu J C 2011 J. Phys. D: Appl. Phys. 44 055401
[14] Liu M, Hou Z L, Fu X J 2012 Acta Phys. Sin. 61 104302 (in Chinese) [刘敏, 侯志林, 傅秀军 2012 61 104302]
[15] Lai Y, Wu Y, Sheng P, Zhang Z Q 2011 Nature Mater. 10 620
[16] Mei J, Ma G, Yang M, Yang Z, Wen W, Sheng P 2012 Nat. Commun. 3 756
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