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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.
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Keywords:
- phononic crystal /
- acoustic band gap /
- lump-mass method /
- frequency response function
[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 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 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 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)]
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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 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 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 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)]
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