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In this paper, a new type of acoustic metamaterial with negative modulus is proposed, and the formation and broadening mechanism of the low frequency bandgap are revealed. The expression of the normalized effective modulus of the structure is derived theoretically. Since the zero value of the effective modulus is closely related to the system parameters, the appropriate parameters can be adjusted to reduce the zero point, and the lower bound of the bandgap is reduced, thus the low-frequency bandgap is realized. The theoretical results show that the elastic modulus of the system is negative and the region of the negative modulus is widened in a certain frequency range, therefore, the widening of the bandgap can be realized through the enlargement of the negative modulus region. This new mechanism for achieving low-frequency bandgap overcomes the shortcomings both in the traditional local resonance with too large additional mass, and in the inertial amplification structures with narrow bandgaps. At the same time, the transmission of this periodic structure obtained by the finite element method is highly consistent with that by the theoretical analysis, with a low-frequency band of 40-180 Hz, from which the new mechanism presented here is verified. This new idea of achieving low-frequency bandgap is of great theoretical significance for controlling low-frequency sound waves.
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Keywords:
- negative modulus /
- acoustic metamaterial /
- low-frequency broadband
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[9] Jaglinski T, Kochmann D, Stone D, Lakes R S 2007 Science 315 620
[10] Lakes R S, Lee T, Bersie A, Wang Y C 2001 Nature 410 565
[11] Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K 2009 Phys. Lett. A 373 4464
[12] Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K 2009 J. Phys.: Conden. Matter 21 175704
[13] Cheng Y, Zhou C, Yuan B G, Wu D J, Wei Q, Liu X J 2015 Nat. Mater. 14 1013
[14] Cheng Y, Xu J Y, Liu X J 2008 Appl. Phys. Lett. 92 051913
[15] Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, Sheng P 2000 Science 289 1734
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[17] 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 物理学报 61 104302]
[18] Wu J, Bai X C, Xiao Y, Geng M X, Yu D L, Wen J H 2016 Acta Phys. Sin. 65 064602 (in Chinese) [吴健, 白晓春, 肖勇, 耿明昕, 郁殿龙, 温激鸿 2016 物理学报 65 064602]
[19] Baravellie, Ruzzene M 2013 J. Sound Vib. 332 6562
[20] Zhang Y, Yin J F, Wen J H, Yu D L 2016 J. Vib. Shock 35 27 (in Chinese) [张印, 尹剑飞, 温激鸿, 郁殿龙 2016 振动与冲击 35 27]
[21] Yilmaz C, Hulbert G M, Kikuchi N 2007 Phys. Rev. B 76 054309
[22] Yilmaz C, Hulbert G M 2010 Phys. Lett. A 374 3576
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[1] Pai P F, Peng H, Jiang S 2014 Int. J. Mech. Sci. 79 195
[2] Gusev V E, Wright O B 2014 New J. Phys. 16 123053
[3] Gao J, Cheng J C, Li B W 2007 Appl. Phys. Lett. 90 111908
[4] Wang Y F, Wang Y S, Wang L T 2014 J. Phys. D: Appl. Phys. 47 015502
[5] Chronopoulos D, Antoniadis I, Collet M, Ichchou M 2015 Wave Motion 58 165
[6] Zhu R, Liu X N, Hu G K, Sun C T, Huang G L 2014 J. Sound Vib. 333 2759
[7] Nouh M, Aldraihem O, Baz A 2015 J. Sound Vib. 341 53
[8] Huang H H, Sun C T, Huang G L 2009 Int. J. Eng. Sci. 47 610
[9] Jaglinski T, Kochmann D, Stone D, Lakes R S 2007 Science 315 620
[10] Lakes R S, Lee T, Bersie A, Wang Y C 2001 Nature 410 565
[11] Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K 2009 Phys. Lett. A 373 4464
[12] Lee S H, Park C M, Seo Y M, Wang Z G, Kim C K 2009 J. Phys.: Conden. Matter 21 175704
[13] Cheng Y, Zhou C, Yuan B G, Wu D J, Wei Q, Liu X J 2015 Nat. Mater. 14 1013
[14] Cheng Y, Xu J Y, Liu X J 2008 Appl. Phys. Lett. 92 051913
[15] Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T, Sheng P 2000 Science 289 1734
[16] Zhang S W, Wu J H 2013 Acta Phys. Sin. 62 134302 (in Chinese) [张思文, 吴九汇 2013 物理学报 62 134302]
[17] 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 物理学报 61 104302]
[18] Wu J, Bai X C, Xiao Y, Geng M X, Yu D L, Wen J H 2016 Acta Phys. Sin. 65 064602 (in Chinese) [吴健, 白晓春, 肖勇, 耿明昕, 郁殿龙, 温激鸿 2016 物理学报 65 064602]
[19] Baravellie, Ruzzene M 2013 J. Sound Vib. 332 6562
[20] Zhang Y, Yin J F, Wen J H, Yu D L 2016 J. Vib. Shock 35 27 (in Chinese) [张印, 尹剑飞, 温激鸿, 郁殿龙 2016 振动与冲击 35 27]
[21] Yilmaz C, Hulbert G M, Kikuchi N 2007 Phys. Rev. B 76 054309
[22] Yilmaz C, Hulbert G M 2010 Phys. Lett. A 374 3576
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