新型负模量声学超结构的低频宽带机理研究

张永燕; 吴九汇; 钟宏民

doi:10.7498/aps.66.094301

摘要

提出了一种具有负模量特性的新型声学超结构，并揭示了其低频带隙的形成及拓宽机理.通过理论推导给出了该新型结构的归一化有效模量表达式，由于有效模量的零值点与系统参数密切相关，可以调节合适的参数使得零值点降低或带隙下界降低，进一步实现低频带隙.理论结果表明，在一定的频率范围内，系统的弹性模量为负且负模量区域进一步拓宽，从而通过负模量区域的放大而拓宽带隙.这种新的实现低频带隙的方法克服了传统局域共振附加质量过大及惯性放大结构带隙较窄的缺点.同时，通过有限元法得到的周期结构的传输率随着结构参数的变化趋势与理论分析的变化趋势基本一致，并得到了约40180 Hz的低频宽带.这种实现低频带隙的新思路对低频声波的控制具有很重要的理论指导意义.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
西安交通大学机械工程学院, 机械结构强度与振动国家重点实验室, 西安 710049;

2.
四川理工学院机械工程学院, 自贡 643000

通信作者: 吴九汇, ejhwu@mail.xjtu.edu.cn

Authors and contacts

1.
School of Mechanical Engineering and State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China;

2.
School of Mechanical Engineering, Sichuan University of Science and Engineering, Zigong 643000, China

Corresponding author: Wu Jiu-Hui, ejhwu@mail.xjtu.edu.cn

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施引文献

[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 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 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 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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