垂直载荷下颗粒物质的声波探测和非线性响应

张攀; 赵雪丹; 张国华; 张祺; 孙其诚; 侯志坚; 董军军

doi:10.7498/aps.65.024501

摘要

对于玻璃珠组成的颗粒介质样品, 本文测量了横波和纵波声速, 同时分析了剪切模量(G)与体积模量(B)的比值(G/B)随压强的变化规律. 结果表明, 在低压强下, 颗粒体系的纵波声速(cL )明显大于横波声速(cT ), 且体系的cL, cT 及G/B均随压强p变化呈幂律标度, 即cL p0.3817, cT p0.2809, G/B p-0.4539, 幂指数与文献[1]中预言的-1/2非常接近, 暗示在我们实验压强范围内的颗粒样品处于L玻璃状态. 此外, 本文还利用快速傅里叶变换法测量了玻璃珠样品中的声学衰减特性及二阶谐波随压强的变化, 发现: 纵波声衰减系数()、接收端二倍频振幅(2 )与基频振幅(1 ) 平方的比值(2/12 ) 均随压强的增大而幂率减小, 分别为 p-0.1879和 2/12 p-0.866.

关键词:

颗粒物质 /
声速 /
衰减系数 /
非线性

Abstract

Owing to their efficient penetration into elastic media, the measurement of sound waves can provide a sensitive probe of both the structural and mechanical properties of the materials through which they propagate. In this work, we first investigate the transversal and longitudinal wave velocities in granular assemblies composed of glass beads under uniaxial load by the time-of-flight method. Then the ratio G/B, (G is the shear modulus and B is the bulk modulus) as a function of pressure is analyzed, based on the theory of classical elasticity. Experimental results show that, with the pressure increasing from 10 to 100 kPa, i) the velocity of longitudinal wave (cL ) is obviously faster than that of transversal one (cT ) in the granular system(the ratio cL/cT is about 1.6), and the cL and cT of the system show power law scaling, i.e. cL p0.3817, cT p0.2809; ii) the ratio G/B decreases in the low pressure range for glass beads packing, i.e. G/B p-0.4539. It is found that the power-law exponent of G/B with pressure is very close to -1/2 (the prediction in 2015 Phys. Rev. Lett. 114 035502), suggesting that the granular system lies in glass L state within the pressure range in our experiment. Furthermore, the fast Fourier transform method is used to study the variation of acoustic attenuation and nonlinear characteristics in granular materials. Our results reveal that the acoustic attenuation coefficient () and the ratio of the second harmonic amplitude ( 2 ) to the square of fundamental amplitude ( 1 ) at the receiving end in the granular system, 2/12, both decrease in power law with the increase of pressure, i.e. p-0.1879, 2/12 p-0.866, respectively.

Keywords:

作者及机构信息

1.
北京科技大学物理系, 北京 100083;

2.
太原理工大学力学学院, 太原 030024;

3.
清华大学水沙科学与水利水电工程国家重点实验室, 北京 100084

通信作者: 张国华, zhguohua@sas.ustb.edu.cn;qcsun@tsinghua.edu.cn ; 孙其诚, zhguohua@sas.ustb.edu.cn;qcsun@tsinghua.edu.cn ;

基金项目: 国家自然科学基金(批准号: 11272048, 51239006)和欧盟Marie Curie国际合作项目(批准号: IRSES-294976)资助的课题.

Authors and contacts

1.
Department of physics, University of Science and Technology Beijing, Beijing 100083, China;

2.
College of Mechanics, Taiyuan University of Technology, Taiyuan 030024, China;

3.
State Key Laboratory for Hydroscience and Engineering, Tsinghua University, Beijing 100084, China

Corresponding author: Zhang Guo-Hua, zhguohua@sas.ustb.edu.cn;qcsun@tsinghua.edu.cn ; Sun Qi-Cheng, zhguohua@sas.ustb.edu.cn;qcsun@tsinghua.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11272048, 51239006) and the European Commission Marie Curie Actions (Grant No. IRSES-294976).

参考文献

[1]	Wang X, Zheng W, Wang L, Xu N 2015 Phys. Rev. Lett. 114 035502
[2]	O'Hern C S, Silbert L E, Liu A J, Nagel S R 2003 Phys. Rev. E 68 011306
[3]	Ikeda A, Berthier L 2015 Phys. Rev. E 92 012309
[4]	Zhang Q, Li Y C, Liu R, Jiang Y M, Hou M Y 2012 Acta Phys. Sin. 61 301 (in Chinese) [张祺, 李寅阊, 刘锐, 蒋亦民, 厚美瑛 2012 物理学报 61 301]
[5]	Zhang Q, Li Y, Hou M, Jiang Y, Liu M 2012 Phys. Rev. E 85 031306
[6]	Merkel A, Tournat V, Gusev V 2014 Phys. Rev. E 90 023206
[7]	Zheng H P 2014 Chin. Phys. B 23 054503
[8]	Jia X, Caroli C, Velicky B 1999 Phys. Rev. Lett. 82 1863
[9]	Lherminier S, Planet R, Simon G, Vanel L, Ramos O 2014 Phys. Rev. Lett. 113 098001
[10]	Xu N 2011 Frontiers of Physics 6 109
[11]	Somfai E, van Hecke M, Ellenbroek W G, Shundyak K, van Saarloos W 2007 Phys. Rev. E 75 020301
[12]	Makse H A, Gland N, Johnson D L, Schwartz L 2004 Phys. Rev. E 70 061302
[13]	Zaccone A, Terentjev E M 2014 J. Appl. Phys. 115 033510
[14]	Zhang Z, Chen G, Zhang D 2014 Chin. Phys. B 23 054302
[15]	Huang D C, Chen W Z, Yang A N, Sun M, Hu F L, Zhao M 2014 Acta Phys. Sin. 63 154502 (in Chinese) [黄德财, 陈伟中, 杨安娜, 孙敏, 胡凤兰, 赵敏 2014 物理学报 63 154502]
[16]	Langlois V, Jia X 2015 Phys. Rev. E 91 022205
[17]	Brunet T, Jia X, Mills P 2008 Phys. Rev. Lett. 101 138001
[18]	Brunet T, Jia X, Johnson P A 2008 Geophys. Res. Lett. 35 L19308
[19]	Deng J, Wang S X, Han D H 2009 J. Geophys. Eng. 6 269
[20]	Miksic A, Alava M J 2013 Phys. Rev. E 88 032207
[21]	Johnson K L 1985 Contact Mechanics (Cambridge: Cambridge University Press)
[22]	Khidas Y, Jia X 2010 Phys. Rev. E 81 021303
[23]	Somfai E, Roux J N, Snoeijer J, van Hecke M, van Saarloos W 2005 Phys. Rev. E 72 021301
[24]	Tighe B 2011 Phys. Rev. Lett. 107 158303
[25]	Basu A, Xu Y, Still T, Arratia P E, Zhang Z, Nordstrom K N, Rieser J M, Gollub J P, Durian D J, Yodh A G 2014 Soft Matter 10 3027
[26]	Goodrich C P, Liu A J, Nagel S R 2014 Nat. Phys. 10 578
[27]	Vitelli V 2010 Soft Matter 6 3007
[28]	Hong J 2005 Phys. Rev. Lett. 94 108001
[29]	Wang P J, Xia J H, Li Y D, Liu C S 2007 Phys. Rev. E 76 041305
[30]	Wang P J, Li Y D, Xia J H, Liu C S 2008 Phys. Rev. E 77 060301
[31]	Thomas Brunet X J, Paul J 2006 French Acoustical Society 2006 Meeting, Paris 475
[32]	Wildenberg S V D, Hecke M V, Jia X 2013 Europhys. Lett. 101 14004
[33]	Renaud G, Calle S, Defontaine M 2010 J. Acoust. Soc. Am. 128 3344

施引文献

[1]	Wang X, Zheng W, Wang L, Xu N 2015 Phys. Rev. Lett. 114 035502
[2]	O'Hern C S, Silbert L E, Liu A J, Nagel S R 2003 Phys. Rev. E 68 011306
[3]	Ikeda A, Berthier L 2015 Phys. Rev. E 92 012309
[4]	Zhang Q, Li Y C, Liu R, Jiang Y M, Hou M Y 2012 Acta Phys. Sin. 61 301 (in Chinese) [张祺, 李寅阊, 刘锐, 蒋亦民, 厚美瑛 2012 物理学报 61 301]
[5]	Zhang Q, Li Y, Hou M, Jiang Y, Liu M 2012 Phys. Rev. E 85 031306
[6]	Merkel A, Tournat V, Gusev V 2014 Phys. Rev. E 90 023206
[7]	Zheng H P 2014 Chin. Phys. B 23 054503
[8]	Jia X, Caroli C, Velicky B 1999 Phys. Rev. Lett. 82 1863
[9]	Lherminier S, Planet R, Simon G, Vanel L, Ramos O 2014 Phys. Rev. Lett. 113 098001
[10]	Xu N 2011 Frontiers of Physics 6 109
[11]	Somfai E, van Hecke M, Ellenbroek W G, Shundyak K, van Saarloos W 2007 Phys. Rev. E 75 020301
[12]	Makse H A, Gland N, Johnson D L, Schwartz L 2004 Phys. Rev. E 70 061302
[13]	Zaccone A, Terentjev E M 2014 J. Appl. Phys. 115 033510
[14]	Zhang Z, Chen G, Zhang D 2014 Chin. Phys. B 23 054302
[15]	Huang D C, Chen W Z, Yang A N, Sun M, Hu F L, Zhao M 2014 Acta Phys. Sin. 63 154502 (in Chinese) [黄德财, 陈伟中, 杨安娜, 孙敏, 胡凤兰, 赵敏 2014 物理学报 63 154502]
[16]	Langlois V, Jia X 2015 Phys. Rev. E 91 022205
[17]	Brunet T, Jia X, Mills P 2008 Phys. Rev. Lett. 101 138001
[18]	Brunet T, Jia X, Johnson P A 2008 Geophys. Res. Lett. 35 L19308
[19]	Deng J, Wang S X, Han D H 2009 J. Geophys. Eng. 6 269
[20]	Miksic A, Alava M J 2013 Phys. Rev. E 88 032207
[21]	Johnson K L 1985 Contact Mechanics (Cambridge: Cambridge University Press)
[22]	Khidas Y, Jia X 2010 Phys. Rev. E 81 021303
[23]	Somfai E, Roux J N, Snoeijer J, van Hecke M, van Saarloos W 2005 Phys. Rev. E 72 021301
[24]	Tighe B 2011 Phys. Rev. Lett. 107 158303
[25]	Basu A, Xu Y, Still T, Arratia P E, Zhang Z, Nordstrom K N, Rieser J M, Gollub J P, Durian D J, Yodh A G 2014 Soft Matter 10 3027
[26]	Goodrich C P, Liu A J, Nagel S R 2014 Nat. Phys. 10 578
[27]	Vitelli V 2010 Soft Matter 6 3007
[28]	Hong J 2005 Phys. Rev. Lett. 94 108001
[29]	Wang P J, Xia J H, Li Y D, Liu C S 2007 Phys. Rev. E 76 041305
[30]	Wang P J, Li Y D, Xia J H, Liu C S 2008 Phys. Rev. E 77 060301
[31]	Thomas Brunet X J, Paul J 2006 French Acoustical Society 2006 Meeting, Paris 475
[32]	Wildenberg S V D, Hecke M V, Jia X 2013 Europhys. Lett. 101 14004
[33]	Renaud G, Calle S, Defontaine M 2010 J. Acoust. Soc. Am. 128 3344

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