Skip to main content
SpringerLink
Log in

Experimental study of nonlinear acoustic bands and propagating breathers in ordered granular media embedded in matrix

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

We experimentally study acoustic pass and stop-bands, and propagating breathers in harmonically excited, ordered granular chains composed of steel beads embedded in three different types of matrix—namely PDMS, polyurethane and geopolymer. Both single and coupled granular chains are tested and the bands and breathers are robustly detected in each case over varying frequency and amplitude ranges. Low-frequency acoustic pass-bands are characterized by pulse-like transmission in the granular media and negligible effective compression, whereas high-frequency stop-bands are characterized exhibit complete filtering of granular media dynamics and strong effective compression. At intermediate frequency ranges we observe the propagation of propagating breathers in the granular chains, in the form of wavetrains of localized wavepackets separated by silent regions. We study the effects of the matrix and the distance between coupled granular chains on the propagation of the breathers, and confirm the robustness of these highly nonlinear responses in this highly discontinuous class of acoustic metamaterials. Moreover, we relate our results to energy transfers between coupled granular chains. Finally, we propose a simplified theoretical model that fully recovers the experimentally detected responses. To the authors’ knowledge this is the first experimental report of acoustic filtering and experimental breathers in practical acoustic nonlinear metamaterials.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Aubry, S.: Breathers in nonlinear lattices: existence, linear stability and quantization. Phys. D 103, 201–250 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bell, J.L., Driemeyer, P.E., Kriven, W.M.: Formation of ceramics from metakaolin-based geopolymers, part II: K-based geopolymer. J. Am. Ceram. Soc. 92(3), 607–615 (2009)

    Article  Google Scholar 

  3. Berman, G.P., Izrailev, F.M.: The Fermi–Pasta–Ulam problem: fifty years of progress. Chaos 15(1), 015104 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  4. Boechler, N., Daraio, C.: An experimental investigation of acoustic band gaps and localization in granular elastic chains. In: Proceedings of the 22nd ASME Biennial Conference on Mechanical Vibration and Noise, San Diego, CA (2009)

  5. Boechler, N., Theocharis, G., Job, S., Kevrekidis, P.G., Porter, M.A., Daraio, C.: Discrete breathers in one-dimensional diatomic granular crystals. Phys. Rev. Lett. 104(24), 244302 (2010)

    Article  ADS  Google Scholar 

  6. Brunhuber, C., Mertens, F.G., Gaididei, Y.: Envelope solitons on anharmonic damped atomic chains. Phys. Rev. E 73(1), 016614 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  7. Coste, C., Falcon, E., Fauve, S.: Solitary waves in a chain of beads under Hertz contact. Phys. Rev. E 56(5), 6104–6117 (1997)

    Article  ADS  Google Scholar 

  8. Daraio, C., Nesterenko, V.F., Herbold, E.B., Jin, S.: Energy trapping and shock disintegration in a composite granular medium. Phys. Rev. Lett. 96(5), 058002 (2006a)

    Article  ADS  Google Scholar 

  9. Daraio, C., Nesterenko, V.F., Herbold, E.B., Jin, S.: Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals. Phys. Rev. E 73(2), 026610 (2006b)

    Article  ADS  Google Scholar 

  10. Dauxois, T., Peyrard, M.: Energy localization in nonlinear lattices. Phys. Rev. Lett. 70(25), 3935–3938 (1993)

    Article  ADS  Google Scholar 

  11. Dauxois, T., Khomeriki, R., Piazza, F., Ruffo, S.: The anti-FPU problem. Chaos 15(1), 015110 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  12. Duxsona, P., Provis, J.L., Lukey, G.C., Mallicoat, S.W., Kriven, W.M., van Deventer, J.S.J.: Understanding the relationship between geopolymer composition, microstructure and mechanical properties. Colloids Surf. A 269, 47–58 (2005)

    Article  Google Scholar 

  13. Engheta, N., Ziolkowski, R.W.: Metamaterials: Physics and Engineering Explorations. Wiley, New York (2006)

    Book  Google Scholar 

  14. Flach, S., Willis, C.R.: Discrete breathers. Phys. Rep. 295, 181–264 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  15. Flach, S., Gorbach, A.V.: Discrete breathers—advances in theory and applications. Phys. Rep. 467(1–3), 1–116 (2008)

    Article  ADS  Google Scholar 

  16. Hasegawa, A.: Generation of a train of soliton pulses by induced modulational instability in optical fibers. Opt. Lett. 9(7), 288–290 (1984)

    Article  ADS  Google Scholar 

  17. Hasan, M.A., Starosvetsky, Y., Vakakis, A.F., Manevitch, L.I.: Nonlinear targeted energy transfer and macroscopic analog of the quantum Landau–Zener effect in coupled granular chains. Phys. D 252, 46–58 (2013a)

    Article  MATH  MathSciNet  Google Scholar 

  18. Hasan, M.A., Cho, S., Remick, K., Vakakis, A.F., McFarland, D.M., Kriven, W.M.: Primary pulse transmission in coupled steel granular chains embedded in PDMS matrix: experiment and modeling. Int. J. Solids Struct. 50(20–21), 3207–3224 (2013b)

    Article  Google Scholar 

  19. Hladky-Hennion, A.-C., Allan, G., de Billy, M.: Localized modes in a one-dimensional diatomic chain of coupled spheres. J. Appl. Phys. 98(5), 054909–054909-7 (2005)

    Article  ADS  Google Scholar 

  20. Hladky-Hennion, A.-C., de Billy, M.: Experimental validation of band gaps and localization in a one-dimensional diatomic phononic crystal. J. Acoust. Soc. Am. 122(5), 2594–2600 (2007)

    Article  ADS  Google Scholar 

  21. James, G.: Nonlinear waves in Newton’s cradle and the discrete p-Schrödinger equation. Math. Models Methods Appl. Sci. 21, 2335–2377 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  22. James, G., Kevrekidis, P.G., Cuevas, J.: Breathers in oscillator chains with Hertzian interactions. Phys. D 251, 39–59 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  23. Jayaprakash, K.R., Starosvetsky, Y., Vakakis, A.F., Peeters, M., Kerschen, G.: Nonlinear normal modes and band zones in granular chains with no pre-compression. Nonlinear Dyn. 63(3), 359–385 (2011)

    Article  MathSciNet  Google Scholar 

  24. Kriven, W.M.: Inorganic polysialates or ’geopolymers. Am. Ceram. Soc. Bull. 89(4), 31–34 (2010)

    Google Scholar 

  25. Lazaridi, A.N., Nesterenko, V.F.: Observation of a new type of solitary waves in a one-dimensional granular medium. J. Appl. Mech. Tech. Phys. 26(3), 405–408 (1985)

    Article  ADS  Google Scholar 

  26. Lydon, J., Jayaprakash, K.R., Ngo, D., Starosvetsky, Y., Vakakis, A.F., Daraio, C.: Frequency bands of strongly nonlinear homogeneous granular systems. Phys. Rev. E 88(1), 012206 (2013)

  27. MacKay, R.: Solitary waves in a chain of beads under Hertz contact. Phys. Lett. A 251(3), 191–192 (1999)

  28. Marquie, P., Bilbault, J.M., Remoissenet, M.: Generation of envelope and hole solitons in an experimental transmission line. Phys. Rev. E 49(1), 828–835 (1994)

    Article  ADS  Google Scholar 

  29. Martínez, P.J., Meister, M., Floría, L.M., Falo, F.: Dissipative discrete breathers: periodic, quasiperiodic, chaotic, and mobile. Chaos 13(2), 610–623 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  30. Martinsson, P.G., Movchan, A.B.: Vibrations of lattice structures and phononic band gaps. Q. J. Mech. Appl. Math. 56(1), 45–64 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  31. Nesterenko, V.F.: Propagation of nonlinear compression pulses in granular media. J. Appl. Mech. Tech. Phys. 24(5), 733–743 (1983)

    Article  ADS  Google Scholar 

  32. Nesterenko, V.: Dynamics of Heterogeneous Materials. Springer, Berlin (2001)

    Book  Google Scholar 

  33. Sen, S., Hong, J., Bang, J., Avalos, E., Doney, R.: Solitary waves in the granular chain. Phys. Rep. 462(2), 21–66 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  34. Sen, S., Mohan, T.R.K.: Dynamics of metastable breathers in nonlinear chains in acoustic vacuum. Phys. Rev. E 79(3), 036603 (2009)

    Article  ADS  Google Scholar 

  35. Shamonina, E., Solymar, L.: Metamaterials: how the subject started. Metamaterials 1(1), 12–18 (2007)

    Article  ADS  Google Scholar 

  36. Starosvetsky, Y., Vakakis, A.F.: Traveling waves and localized modes in one-dimensional homogeneous granular chains with no precompression. Phys. Rev. E 82(2), 026603 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  37. Starosvetsky, Y., Jayaprakash, K.R., Vakakis, A.F.: Scattering of solitary waves and excitation of transient breathers in granular media by light intruders and no precompression. J. Appl. Mech. 79(1), 011001–011001 (2011)

    Article  Google Scholar 

  38. Starosvetsky, Y., Hasan, M.A., Vakakis, A.F., Manevitch, L.I.: Strongly nonlinear beat phenomena and energy exchanges in weakly coupled granular chains on elastic foundations. SIAM J. Appl. Math. 72(1), 337–361 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  39. Starosvetsky, Y., Hasan, M.A., Vakakis, A.F.: Nonlinear pulse equipartition in weakly coupled ordered granular chains with no precompression. J. Comput. Nonlinear Dyn. 8(3), 034504–034504 (2013)

    Article  Google Scholar 

  40. Szelengowicz, I., Hasan, M.A., Starosvetsky, Y., Vakakis, A., Daraio, C.: Energy equipartition in two-dimensional granular systems with spherical intruders. Phys. Rev. E 87(3), 032204 (2013)

    Article  ADS  Google Scholar 

  41. Theocharis, G., Kavousanakis, M., Kevrekidis, P.G., Daraio, C., Porter, M.A., Kevrekidis, I.G.: Localized breathing modes in granular crystals with defects. Phys. Rev. E 80(6), 066601 (2009)

    Article  ADS  Google Scholar 

  42. Theocharis, G., Boechler, N., Kevrekidis, P.G., Job, S., Porter, M.A., Daraio, C.: Intrinsic energy localization through discrete gap breathers in one-dimensional diatomic granular crystals. Phys. Rev. E 82(5), 056604 (2010)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work was funded by MURI grant US ARO W911NF-09-1-0436. Dr. David Stepp is the grant monitor.

Author information

Authors and Affiliations

  1. Department of Mechanical Science and Engineering, University of Illinois at Urbana – Champaign, 1206 West Green Street, Urbana, IL, 61822, USA

    M. Arif Hasan, Shinhu Cho, Kevin Remick & Alexander F. Vakakis

  2. Department of Aerospace Engineering, University of Illinois at Urbana – Champaign, 319L Talbot Lab, 104 S. Wright Street, Urbana, IL, 61801, USA

    D. Michael McFarland

  3. Department of Materials Science and Engineering, University of Illinois at Urbana – Champaign, 1304 W. Green St., Urbana, IL, 61801, USA

    Waltraud M. Kriven

Authors
  1. M. Arif Hasan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shinhu Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kevin Remick
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alexander F. Vakakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. D. Michael McFarland
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Waltraud M. Kriven
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Arif Hasan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hasan, M.A., Cho, S., Remick, K. et al. Experimental study of nonlinear acoustic bands and propagating breathers in ordered granular media embedded in matrix. Granular Matter 17, 49–72 (2015). https://doi.org/10.1007/s10035-014-0536-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-014-0536-y

Keywords

Search

Navigation