Long Wavelength Coherent Pulse of Sound Propagating in Granular Media
A mechanical wave or vibration propagating through
granular media exhibits a specific signature in time. A coherent
pulse or wavefront arrives first with multiply scattered waves (coda)
arriving later. The coherent pulse is micro-structure independent i.e.
it depends only on the bulk properties of the disordered granular
sample, the sound wave velocity of the granular sample and hence
bulk and shear moduli. The coherent wavefront attenuates (decreases
in amplitude) and broadens with distance from its source. The
pulse attenuation and broadening effects are affected by disorder
(polydispersity; contrast in size of the granules) and have often been
attributed to dispersion and scattering. To study the effect of disorder
and initial amplitude (non-linearity) of the pulse imparted to the
system on the coherent wavefront, numerical simulations have been
carried out on one-dimensional sets of particles (granular chains).
The interaction force between the particles is given by a Hertzian
contact model. The sizes of particles have been selected randomly
from a Gaussian distribution, where the standard deviation of this
distribution is the relevant parameter that quantifies the effect of
disorder on the coherent wavefront. Since, the coherent wavefront is
system configuration independent, ensemble averaging has been used
for improving the signal quality of the coherent pulse and removing
the multiply scattered waves. The results concerning the width of the
coherent wavefront have been formulated in terms of scaling laws. An
experimental set-up of photoelastic particles constituting a granular
chain is proposed to validate the numerical results.
[1] P. Shearer, Introduction to Seismology. Cambridge
University Press, 2009. (Online). Available:
https://books.google.nl/books?id=VV0mV4lF0RUC.
[2] A. M. Dainty and M. Toksz, “Seismic codas on the earth and
the moon: a comparison,” Physics of the Earth and Planetary
Interiors, vol. 26, no. 4, pp. 250 – 260, 1981. (Online). Available:
http://www.sciencedirect.com/science/article/pii/0031920181900297. [3] J. O’Donovan, E. Ibraim, C. O’Sullivan, S. Hamlin, D. Muir Wood,
and G. Marketos, “Micromechanics of seismic wave propagation in
granular materials,” Granular Matter, vol. 18, no. 3, p. 56, Jun 2016.
(Online). Available: https://doi.org/10.1007/s10035-015-0599-4.
[4] P. Sheng, Intoduction to Wave Scattering, Localization and Mesoscopic
Phenomena, ser. Springer Series in Materials Science. Springer, 2006.
(Online). Available: https://doi.org/10.1007/3-540-29156-3.
[5] V. Langlois and X. Jia, “Sound pulse broadening in stressed granular
media,” Phys. Rev. E, vol. 91, p. 022205, Feb 2015. (Online). Available:
https://link.aps.org/doi/10.1103/PhysRevE.91.022205
[6] I. G¨uven, “Hydraulical and acoustical properties of porous sintered glass
bead systems: experiments, theory, & simulations,” Ph.D. dissertation,
Enschede, 2016. (Online). Available: http://doc.utwente.nl/100546/.
[7] X. Jia, “Codalike multiple scattering of elastic waves in dense granular
media,” Phys. Rev. Lett., vol. 93, p. 154303, Oct 2004. (Online).
Available: http://link.aps.org/doi/10.1103/PhysRevLett.93.154303.
[8] X. Jia, C. Caroli, and B. Velicky, “Ultrasound propagation
in externally stressed granular media,” Phys. Rev. Lett.,
vol. 82, pp. 1863–1866, Mar 1999. (Online). Available:
http://link.aps.org/doi/10.1103/PhysRevLett.82.1863.
[9] H. A. Makse, N. Gland, D. L. Johnson, and L. Schwartz, “Granular
packings: Nonlinear elasticity, sound propagation, and collective relaxation
dynamics,” Phys. Rev. E, vol. 70, p. 061302, Dec 2004. (Online).
Available: http://link.aps.org/doi/10.1103/PhysRevE.70.061302.
[10] R. K. Shrivastava and S. Luding, “Effect of disorder on bulk sound
wave speed: a multiscale spectral analysis,” Nonlinear Processes in
Geophysics, vol. 24, no. 3, pp. 435–454, 2017. (Online). Available:
https://www.nonlin-processes-geophys.net/24/435/2017/.
[11] V. Nesterenko, “Propagation of nonlinear compression pulses in granular
media,” J. Appl. Mech. Tech. Phys., vol. 24, pp. 733–743, March 1983.
[12] E. T. Owens and K. E. Daniels, “Sound propagation and force
chains in granular materials,” EPL (Europhysics Letters), vol. 94,
no. 5, p. 54005, 2011. (Online). Available: http://stacks.iop.org/0295-
5075/94/i=5/a=54005.
[13] E. Somfai, J.-N. Roux, J. H. Snoeijer, M. van Hecke, and W. van
Saarloos, “Elastic wave propagation in confined granular systems,”
Phys. Rev. E, vol. 72, p. 021301, Aug 2005. (Online). Available:
http://link.aps.org/doi/10.1103/PhysRevE.72.021301.
[14] T. S. Majmudar and R. P. Behringer, “Contact force measurements
and stress-induced anisotropy in granular materials,” Nature, vol.
435, no. 1079, pp. 1079–1082, 06 2005. (Online). Available:
http://dx.doi.org/10.1038/nature03805.
[15] B. P. Lawney and S. Luding, “Massdisorder effects on the frequency
filtering in onedimensional discrete particle systems,” AIP Conference
Proceedings, vol. 1542, no. 1, pp. 535–538, 2013. (Online). Available:
http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4811986.
[16] Shrivastava, Rohit Kumar and Luding, Stefan, “Wave propagation
of spectral energy content in a granular chain,” EPJ
Web Conf., vol. 140, p. 02023, 2017. (Online). Available:
https://doi.org/10.1051/epjconf/201714002023.
[17] L. D. Landau and E. M. Lifshitz, Theory of elasticity. Pergamon Press,
1970.
[18] P. W. Anderson, “Absence of diffusion in certain random lattices,”
Phys. Rev., vol. 109, pp. 1492–1505, Mar 1958. (Online). Available:
http://link.aps.org/doi/10.1103/PhysRev.109.1492.
[19] J. O’Donovan, C. O’Sullivan, G. Marketos, and D. Muir Wood,
“Analysis of bender element test interpretation using the discrete
element method,” Granular Matter, vol. 17, no. 2, pp. 197–216, 2015.
(Online). Available: http://dx.doi.org/10.1007/s10035-015-0552-6.
[20] E. W. Weisstein, “Tree. From MathWorld—A Wolfram Web
Resource,” last visited on 6/9/2017. (Online). Available:
http://mathworld.wolfram.com/GaussianFunction.html.
[21] O. Mouraille, W. A. Mulder, and S. Luding, “Sound wave acceleration
in granular materials,” Journal of Statistical Mechanics: Theory and
Experiment, vol. 2006, no. 07, p. P07023, 2006. (Online). Available:
http://stacks.iop.org/1742-5468/2006/i=07/a=P07023.
[1] P. Shearer, Introduction to Seismology. Cambridge
University Press, 2009. (Online). Available:
https://books.google.nl/books?id=VV0mV4lF0RUC.
[2] A. M. Dainty and M. Toksz, “Seismic codas on the earth and
the moon: a comparison,” Physics of the Earth and Planetary
Interiors, vol. 26, no. 4, pp. 250 – 260, 1981. (Online). Available:
http://www.sciencedirect.com/science/article/pii/0031920181900297. [3] J. O’Donovan, E. Ibraim, C. O’Sullivan, S. Hamlin, D. Muir Wood,
and G. Marketos, “Micromechanics of seismic wave propagation in
granular materials,” Granular Matter, vol. 18, no. 3, p. 56, Jun 2016.
(Online). Available: https://doi.org/10.1007/s10035-015-0599-4.
[4] P. Sheng, Intoduction to Wave Scattering, Localization and Mesoscopic
Phenomena, ser. Springer Series in Materials Science. Springer, 2006.
(Online). Available: https://doi.org/10.1007/3-540-29156-3.
[5] V. Langlois and X. Jia, “Sound pulse broadening in stressed granular
media,” Phys. Rev. E, vol. 91, p. 022205, Feb 2015. (Online). Available:
https://link.aps.org/doi/10.1103/PhysRevE.91.022205
[6] I. G¨uven, “Hydraulical and acoustical properties of porous sintered glass
bead systems: experiments, theory, & simulations,” Ph.D. dissertation,
Enschede, 2016. (Online). Available: http://doc.utwente.nl/100546/.
[7] X. Jia, “Codalike multiple scattering of elastic waves in dense granular
media,” Phys. Rev. Lett., vol. 93, p. 154303, Oct 2004. (Online).
Available: http://link.aps.org/doi/10.1103/PhysRevLett.93.154303.
[8] X. Jia, C. Caroli, and B. Velicky, “Ultrasound propagation
in externally stressed granular media,” Phys. Rev. Lett.,
vol. 82, pp. 1863–1866, Mar 1999. (Online). Available:
http://link.aps.org/doi/10.1103/PhysRevLett.82.1863.
[9] H. A. Makse, N. Gland, D. L. Johnson, and L. Schwartz, “Granular
packings: Nonlinear elasticity, sound propagation, and collective relaxation
dynamics,” Phys. Rev. E, vol. 70, p. 061302, Dec 2004. (Online).
Available: http://link.aps.org/doi/10.1103/PhysRevE.70.061302.
[10] R. K. Shrivastava and S. Luding, “Effect of disorder on bulk sound
wave speed: a multiscale spectral analysis,” Nonlinear Processes in
Geophysics, vol. 24, no. 3, pp. 435–454, 2017. (Online). Available:
https://www.nonlin-processes-geophys.net/24/435/2017/.
[11] V. Nesterenko, “Propagation of nonlinear compression pulses in granular
media,” J. Appl. Mech. Tech. Phys., vol. 24, pp. 733–743, March 1983.
[12] E. T. Owens and K. E. Daniels, “Sound propagation and force
chains in granular materials,” EPL (Europhysics Letters), vol. 94,
no. 5, p. 54005, 2011. (Online). Available: http://stacks.iop.org/0295-
5075/94/i=5/a=54005.
[13] E. Somfai, J.-N. Roux, J. H. Snoeijer, M. van Hecke, and W. van
Saarloos, “Elastic wave propagation in confined granular systems,”
Phys. Rev. E, vol. 72, p. 021301, Aug 2005. (Online). Available:
http://link.aps.org/doi/10.1103/PhysRevE.72.021301.
[14] T. S. Majmudar and R. P. Behringer, “Contact force measurements
and stress-induced anisotropy in granular materials,” Nature, vol.
435, no. 1079, pp. 1079–1082, 06 2005. (Online). Available:
http://dx.doi.org/10.1038/nature03805.
[15] B. P. Lawney and S. Luding, “Massdisorder effects on the frequency
filtering in onedimensional discrete particle systems,” AIP Conference
Proceedings, vol. 1542, no. 1, pp. 535–538, 2013. (Online). Available:
http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4811986.
[16] Shrivastava, Rohit Kumar and Luding, Stefan, “Wave propagation
of spectral energy content in a granular chain,” EPJ
Web Conf., vol. 140, p. 02023, 2017. (Online). Available:
https://doi.org/10.1051/epjconf/201714002023.
[17] L. D. Landau and E. M. Lifshitz, Theory of elasticity. Pergamon Press,
1970.
[18] P. W. Anderson, “Absence of diffusion in certain random lattices,”
Phys. Rev., vol. 109, pp. 1492–1505, Mar 1958. (Online). Available:
http://link.aps.org/doi/10.1103/PhysRev.109.1492.
[19] J. O’Donovan, C. O’Sullivan, G. Marketos, and D. Muir Wood,
“Analysis of bender element test interpretation using the discrete
element method,” Granular Matter, vol. 17, no. 2, pp. 197–216, 2015.
(Online). Available: http://dx.doi.org/10.1007/s10035-015-0552-6.
[20] E. W. Weisstein, “Tree. From MathWorld—A Wolfram Web
Resource,” last visited on 6/9/2017. (Online). Available:
http://mathworld.wolfram.com/GaussianFunction.html.
[21] O. Mouraille, W. A. Mulder, and S. Luding, “Sound wave acceleration
in granular materials,” Journal of Statistical Mechanics: Theory and
Experiment, vol. 2006, no. 07, p. P07023, 2006. (Online). Available:
http://stacks.iop.org/1742-5468/2006/i=07/a=P07023.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:76575", author = "Rohit Kumar Shrivastava and Amalia Thomas and Nathalie Vriend and Stefan Luding", title = "Long Wavelength Coherent Pulse of Sound Propagating in Granular Media", abstract = "A mechanical wave or vibration propagating through
granular media exhibits a specific signature in time. A coherent
pulse or wavefront arrives first with multiply scattered waves (coda)
arriving later. The coherent pulse is micro-structure independent i.e.
it depends only on the bulk properties of the disordered granular
sample, the sound wave velocity of the granular sample and hence
bulk and shear moduli. The coherent wavefront attenuates (decreases
in amplitude) and broadens with distance from its source. The
pulse attenuation and broadening effects are affected by disorder
(polydispersity; contrast in size of the granules) and have often been
attributed to dispersion and scattering. To study the effect of disorder
and initial amplitude (non-linearity) of the pulse imparted to the
system on the coherent wavefront, numerical simulations have been
carried out on one-dimensional sets of particles (granular chains).
The interaction force between the particles is given by a Hertzian
contact model. The sizes of particles have been selected randomly
from a Gaussian distribution, where the standard deviation of this
distribution is the relevant parameter that quantifies the effect of
disorder on the coherent wavefront. Since, the coherent wavefront is
system configuration independent, ensemble averaging has been used
for improving the signal quality of the coherent pulse and removing
the multiply scattered waves. The results concerning the width of the
coherent wavefront have been formulated in terms of scaling laws. An
experimental set-up of photoelastic particles constituting a granular
chain is proposed to validate the numerical results.", keywords = "Discrete elements, Hertzian Contact, polydispersity,
weakly nonlinear, wave propagation.", volume = "11", number = "10", pages = "1719-8", }
