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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.
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Keywords:
- granular matter /
- acoustic velocity /
- acoustic attenuation /
- nonlinear
[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 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 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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[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 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 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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