Granular Matter

, Volume 10, Issue 1, pp 13–20 | Cite as

Solitary wave trains in granular chains: experiments, theory and simulations

  • Stéphane JobEmail author
  • Francisco Melo
  • Adam Sokolow
  • Surajit Sen


The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes. We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease. The characteristic time is mainly a function involving the grains’ masses and the striker mass. Numerical calculations and experiments corroborate these findings.


One-dimensional granular chain Solitary wave Stepped chain Pulses train formation 


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  1. 1.
    Nesterenko V.F. (1983). Propagation of nonlinear compression pulses in granular media. J. Appl. Mech. Technol. Phys. 24: 733–743 CrossRefADSGoogle Scholar
  2. 2.
    Lazaridi A.N. and Nesterenko V.F. (1985). Observation of a new type of solitary waves in a one-dimensional granular medium. J. Appl. Mech. Technol. Phys. 26: 405–408 CrossRefADSGoogle Scholar
  3. 3.
    Sinkovits R.S. and Sen S. (1995). Nonlinear dynamics in granular columns. Phys. Rev. Lett. 74: 2686 CrossRefADSGoogle Scholar
  4. 4.
    Sen S. and Sinkovits R.S. (1996). Sound propagation in impure granular columns. Phys. Rev. E 54: 6857 CrossRefADSGoogle Scholar
  5. 5.
    Coste C., Falcon E. and Fauve S. (1997). Solitary waves in a chain of beads under Hertz contact. Phys. Rev. E 56: 6104–6117 CrossRefADSGoogle Scholar
  6. 6.
    Sen S., Manciu M. and Wright J.D. (1998). Solitonlike pulses in perturbed and driven Hertzian chains and their possible applications in detecting buried impurities. Phys. Rev. E 57: 2386–2397 CrossRefADSGoogle Scholar
  7. 7.
    Nesterenko V.F. (2001). Dynamics of Heterogeneous Materials. Springer, New York Google Scholar
  8. 8.
    Sen S. and Manciu M. (2001). Solitary wave dynamics in generalized Hertz chains: An improved solution of the equation of motion. Phys. Rev. E 64: 056605 CrossRefADSGoogle Scholar
  9. 9.
    Job S., Melo F., Sokolow A. and Sen S. (2005). How solitary waves interact with boundaries in a 1d granular medium. Phys. Rev. Lett. 94: 178002 CrossRefADSGoogle Scholar
  10. 10.
    Sokolow A., Bittle E.G. and Sen S. (2007). Formation of solitary wave trains in granular alignments. Europhys. Lett. 77: 24002 CrossRefADSGoogle Scholar
  11. 11.
    Herrmann F. and Schmälzle P. (1981). Simple explanation of a well-known collision experiment. Am. J. Phys. 49: 761–764 CrossRefADSGoogle Scholar
  12. 12.
    Herrmann F. and Seitz M. (1982). How does the ball-chain work?. Am. J. Phys. 50: 977–981 CrossRefADSGoogle Scholar
  13. 13.
    Falcon E., Laroche C., Fauve S. and Coste C. (1998). Collision of a 1D column of beads with a wall. Eur. Phys. J. B 5: 111–131 CrossRefADSGoogle Scholar
  14. 14.
    Nesterenko V.F., Daraio C., Herbold E. and Jin S. (2005). Anomalous wave reflection at the interface of two strongly nonlinear granular media. Phys. Rev. Lett. 95: 158702 CrossRefADSGoogle Scholar
  15. 15.
    Daraio C., Nesterenko V.F., Herbold E.B. and Jin S. (2006). Energy trapping and shock disintegration in a composite granular medium. Phys. Rev. Lett. 96: 058002 CrossRefADSGoogle Scholar
  16. 16.
    Daraio C., Nesterenko V.F., Herbold E.B. and Jin S. (2006). Pulse mitigation by a composite discrete medium. J. Phys. IV 134: 473–479 CrossRefGoogle Scholar
  17. 17.
    Nesterenko V.F. (1994). Solitary waves in discrete media with anomalous compressibility and similar to “sonic vacuum”. J. Phys. IV 4: C8–729 CrossRefGoogle Scholar
  18. 18.
    Nesterenko V.F., Lazaridi A.N. and Sibiryakov E.B. (1995). The decay of soliton at the contact of two “acoustic vacuums”. J. Appl. Mech. Technol. Phys. 36: 166–168 CrossRefADSGoogle Scholar
  19. 19.
    Sen S., Manciu F.S. and Manciu M. (2001). Thermalizing an impulse. Phys. A 299: 551 zbMATHCrossRefGoogle Scholar
  20. 20.
    Sokolow A., Pfannes J.M., Doney R.L., Nakagawa M., Agui J.H. and Sen S. (2005). Absorption of short duration pulses by small, scalable, tapered granular chains. Appl. Phys. Lett. 87: 254104 CrossRefGoogle Scholar
  21. 21.
    Doney R.L. and Sen S. (2005). Impulse absorption by tapered horizontal alignments of elastic spheres. Phys. Rev. E 72: 041304 CrossRefADSGoogle Scholar
  22. 22.
    Melo F., Job S., Santibanez F. and Tapia F. (2006). Experimental evidence of shock mitigation in a Hertzian tapered chain. Phys. Rev. E 73: 041305 CrossRefADSGoogle Scholar
  23. 23.
    Doney R.L. and Sen S. (2006). The decorated, tapered, highly nonlinear granular chain. Phys. Rev. Lett 97: 155502 CrossRefADSGoogle Scholar
  24. 24.
    Hertz H. (1881). Über die berührung fester elastischer körper. J. Reine Angew. Math. 92: 156–171 Google Scholar
  25. 25.
    Chatterjee A. (1999). Asymptotic solution for solitary waves in a chain of elastic spheres. Phys. Rev. E 59: 5912–5919 CrossRefADSGoogle Scholar
  26. 26.
    Landau L.D., Lifshitz E.M. (1967) Theorie de l’élasticité. Mir, Moscou, 2nd edn (in French)Google Scholar
  27. 27.
    Daraio C., Nesterenko V., Jin S. (2004) Strongly nonlinear waves in 3d phononic crystals. In: Furnish, M.D., Gupta, Y.M., Forbes, J.W. (eds.) Shock compression of condensend matter—2003, Proceedings of the conference of the American physical society topical group on shock compression of condensed matter, vol 706, pp. 197–200, AIPGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Stéphane Job
    • 1
    Email author
  • Francisco Melo
    • 2
  • Adam Sokolow
    • 3
  • Surajit Sen
    • 3
  1. 1.SupmecaSaint-OuenFrance
  2. 2.Departamento de FísicaUSACH and CIMATSantiagoChile
  3. 3.Department of PhysicsState University of New York at BuffaloBuffaloUSA

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