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一维指数形变截面有限周期声子晶体的研究

付志强 林书玉 陈时 鲜晓军 张小丽 王勇

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一维指数形变截面有限周期声子晶体的研究

付志强, 林书玉, 陈时, 鲜晓军, 张小丽, 王勇

Investigation of one-dimensional finite phononic crystal with exponential section

Fu Zhi-Qiang, Lin Shu-Yu, Chen Shi, Xian Xiao-Jun, Zhang Xiao-Li, Wang Yong
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  • 本文利用集中质量法对弹性纵波在一维指数形截面有限周期声子晶体中的传播进行了研究, 得到了频率响应函数的表达式. 与一维等截面的声子晶体相比, 指数形变截面声子晶体带隙内的衰减值随着输出端截面积的增大而减小, 同时带隙的起始频率降低而截止频率升高, 也即带隙的宽度会得到拓展. 晶格常数和材料组份比变化时, 变截面声子晶体带隙的起始频率和截止频率的变化趋势与等截面时的声子晶体相同. 希望本文的研究能够推动声子晶体在减振降噪等领域中的应用.
    In this paper, we study the propagation of elastic longitudinal wave in one-dimensional (1D) finite periodic phononic crystal with exponential section, and obtain the expression of frequency response function. Comparing the 1D phononic crystal with constant section, we find that the value of attenuation inside the band gap decreases quickly as the cross-sectional area of output and increases, at the same time, the initial frequency decreases and the cut-off frequency increases, i.e. the width of the band gap will increase. The effects of the lattice constant and the filling fraction on band gap are also analyzed. The change trends of the initial frequency and cut-off frequency are consistent with those of constant section. We hope that the investigation of this paper will be helpful for the phononic crystal in practical application such as vibration shield.
    • 基金项目: 陕西师范大学研究生创新基金(批准号: 2011CXB012)和国家自然科学基金(批准号: 11174192)资助的课题.
    • Funds: Project supported by the Innovation Funds of Graduate Programs of Shaanxi Normal University (Grant No. 2011CXB012), and the National Natural Science Foundation of China (Grant No. 11174192).
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    Wang G, Wen J, Wen X 2005 Phys. Rev. B 71 104302

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    Wang G, Wen X, Wen J, Shao L, Liu Y 2004 Phy. Rev. Lett. 93 154302

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    Wen J H, Wang G, Yu D L, Zhao H G, Liu Y Z, Wen X S 2007 Science in China E 37 1126 (in Chinese) [温激鸿, 王刚, 郁殿龙, 赵宏刚, 刘耀宗, 温熙森 2007 中国科学E辑 37 1126]

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    Liang B, Yuan B, Cheng J C 2009 Phys. Rev. Lett. 103 104301

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    Liang B, Guo X S, Tu J, Zhang D, Cheng J C 2010 Nature Mater. 9 989

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  • [1]

    John S 1987 Phys. Rev. Lett. 58 2486

    [2]

    Yablonovitch E 1987 Phys. Rev. Lett. 58 2059

    [3]

    Kushwaha M S, Halevi P, Dobrzynski L, Djafari-Rouhani B 1993 Phys. Rev. Lett. 71 2022

    [4]

    Sigalas M M, Economou E N 1992 J. Sound Vib. 158 377

    [5]

    Sigalas M M, Soukoulis C M 1995 Phys. Rev. B 51 2780

    [6]

    Kushwaha M S, Djafari-Rouhani B 2000 J. Appl. Phys. 88 2877

    [7]

    Mizuno S, Tamura S 1992 Phys. Rev. B 45 734

    [8]

    Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, P Sheng 2000 Science 289 1734

    [9]

    Chen S, Lin S, Wang Z 2010 Solid State Commun. 150 285

    [10]

    Wu F G, Liu Y Y 2002 Acta Phys. Sin. 51 1434 (in Chinese) [吴福根, 刘有延 2002 物理学报 51 1434]

    [11]

    Jensen J S 2003 J. Sound Vib. 266 1053

    [12]

    Wen J H, Wang G, Liu Y Z, Yu D L 2004 Acta Phys. Sin. 53 3384 (in Chinese) [温激鸿, 王刚, 刘耀宗, 郁殿龙 2004 物理学报 53 3384]

    [13]

    Wang G, Wen J, Liu Y, Wen X 2004 Phys. Rev. B 69 184302

    [14]

    Wang G, Wen J, Wen X 2005 Phys. Rev. B 71 104302

    [15]

    Wang G, Wen X, Wen J, Shao L, Liu Y 2004 Phy. Rev. Lett. 93 154302

    [16]

    Wen J H, Wang G, Yu D L, Zhao H G, Liu Y Z, Wen X S 2007 Science in China E 37 1126 (in Chinese) [温激鸿, 王刚, 郁殿龙, 赵宏刚, 刘耀宗, 温熙森 2007 中国科学E辑 37 1126]

    [17]

    Liang B, Yuan B, Cheng J C 2009 Phys. Rev. Lett. 103 104301

    [18]

    Liang B, Guo X S, Tu J, Zhang D, Cheng J C 2010 Nature Mater. 9 989

    [19]

    Cao Y J, Dong C H, Zhou P Q 2006 Acta Phys. Sin. 55 6470 (in Chinese) [曹永军, 董纯红, 周培勤 2006 物理学报 55 6470]

    [20]

    Huang K 2009 Solid State Physics (Beijing: Peking University Press) (in Chinese) [黄昆 2009 固体物理学(北京: 北京大学出版社)]

计量
  • 文章访问数:  5874
  • PDF下载量:  568
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-02-13
  • 修回日期:  2012-03-21

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