Skip to main content
Log in

Frequency- and Amplitude-Dependent Transmission of Stress Waves in Curved One-Dimensional Granular Crystals Composed of Diatomic Particles

  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

We study the stress wave propagation in curved chains of particles (granular crystals) confined by bent elastic guides. We report the frequency- and amplitude-dependent filtering of transmitted waves in relation to various impact conditions and geometrical configurations. The granular crystals studied consist of alternating cylindrical and spherical particles pre-compressed with variable static loads. First, we excite the granular crystals with small-amplitude, broadband perturbations using a piezoelectric actuator to generate oscillatory elastic waves. We find that the linear frequency spectrum of the transmitted waves creates pass- and stop-bands in agreement with the theoretical dispersion relation, demonstrating the frequency-dependent filtering of input excitations through the diatomic granular crystals. Next, we excite high-amplitude nonlinear pulses in the crystals using striker impacts. Experimental tests verify the formation and propagation of highly nonlinear solitary waves that exhibit amplitude-dependent attenuation. We show that the wave propagation can be easily tuned by manipulating the pre-compression imposed to the chain or by varying the initial curvature of the granular chains. We use a combined discrete element (DE) and finite element (FE) numerical model to simulate the propagation of both dispersive linear waves and compactly-supported highly nonlinear waves. We find that the tunable, frequency- and amplitude-dependent filtering of the incoming signals results from the close interplay between the granular particles and the soft elastic media. The findings in this study suggest that hybrid structures composed of granular particles and linear elastic media can be employed as new passive acoustic filtering materials that selectively transmit or mitigate excitations in a desired range of frequencies and amplitudes.

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

Access this article

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

Similar content being viewed by others

References

  1. Nesterenko VF (1983) Propagation of nonlinear compression pulses in granular media. J Appl Mech Tech Phys 24:733–743

    Article  Google Scholar 

  2. Nesterenko VF (2001) Dynamics of Heterogeneous Materials. Springer-Verlag New York, Inc, New York

    Book  Google Scholar 

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

    Article  Google Scholar 

  4. Chatterjee A (1999) Asymptotic solution for solitary waves in a chain of elastic spheres. Physical Review E 59(5):5912–5919

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. Daraio C, Nesterenko VF, Herbold EB, Jin S (2005) Strongly nonlinear waves in a chain of Teflon beads. Physical Review E 72(1):016603

    Article  Google Scholar 

  7. Jaeger HM, Nagel SR, Behringer RP (1996) Granular solids, liquids, and gases. Rev Mod Phys 68(4):1259–1273

    Article  Google Scholar 

  8. Sokolow A, Bittle EG, Sen S (2007) Solitary wave train formation in Hertzian chains. EPL (Europhysics Letters) 77(2):24002

    Article  Google Scholar 

  9. Manciu M, Sen S, Hurd AJ (2001) Crossing of identical solitary waves in a chain of elastic beads. Physical Review E 63(1):016614

    Article  Google Scholar 

  10. Herbold EB, Nesterenko VF (2007) Shock wave structure in a strongly nonlinear lattice with viscous dissipation. Physical Review E 75(2):021304

    Google Scholar 

  11. Molinari A, Daraio C (2009) Stationary shocks in periodic highly nonlinear granular chains. Physical Review E 80:056602

    Google Scholar 

  12. Avalos E, Sen S (2009) How solitary waves collide in discrete granular alignments. Physical Review E 79(4):046607

    Article  Google Scholar 

  13. Santibanez F, Munoz R, Caussarieu A, Job S, Melo F (2011) Experimental evidence of solitary wave interaction in Hertzian chains. Physical Review E 84(2):026604

    Article  Google Scholar 

  14. Sen S, Mohan TRK, Donald P, Visco J, Swaminathan S, Sokolow A, Avalos E, Nakagawa M (2005) Using Mechanical Energy as a Probe for the Detection and Imaging of shallow Buried Inclusions in Dry Granular Beds. Int J Mod Phys B (Singapore) 19(18):2951–2973

    Article  Google Scholar 

  15. Spadoni A, Daraio C (2010) Generation and control of sound bullets with a nonlinear acoustic lens. Proc Natl Acad Sci U S A(107), pp. 7230-7234.

  16. Sen S, Manciu FS, Manciu M (2001) Thermalizing an impulse. Physica A: Statistical Mechanics and its Applications 299(3–4):551–558

    Article  MATH  Google Scholar 

  17. Hong J (2005) Universal power-law decay of the impulse energy in granular protectors. Physical Review Letters, 94,108001(10)

  18. Daraio C, Nesterenko VF, Herbold EB, Jin S (2006) Energy trapping and shock disintegration in a composite granular medium. Phys Rev Lett 96(5):058002

    Article  Google Scholar 

  19. Melo F, Job S, Santibanez F, Tapia F (2006) Experimental evidence of shock mitigation in a Hertzian tapered chain. Physical Review E 73(4):041305

    Article  Google Scholar 

  20. Fraternali F, Porter MA, Daraio C (2009) Optimal Design of Composite Granular Protectors. Mech Adv Mater Struct 17(1):1–19

    Article  Google Scholar 

  21. Khatri D, Rizzo P, Daraio C (2008) Highly nonlinear waves’ sensor technology for highway infrastructures. SPIE Smart Structures/NDE, 15th annual international symposium San Diego, CA, 6934-6925

  22. Yang J, Silvestro C, Sangiorgio S, Borkowski S, Ebramzadeh E, De Nardo L, Daraio C (2012) Nondestructive evaluation of orthopedic implant stability in THA using highly nonlinear solitary waves. Smart Materials and Structures 21:012001

    Article  Google Scholar 

  23. Yang J, Sangiorgio S, Silvestro C, De Nardo L, Daraio C, Ebramzadeh E (2012) Site-specific quantification of bone quality using highly nonlinear solitary waves, Journal of Biomechanical Engineering (in print).

  24. Herbold E, Kim J, Nesterenko V, Wang S, Daraio C (2009) Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap. Acta Mechanica 205(1):85–103

    Article  MATH  Google Scholar 

  25. Boechler N, Yang J, Theocharis G, Kevrekidis PG, Daraio C (2011) Tunable vibrational band gaps in one-dimensional diatomic granular crystals with three-particle unit cells. J Appl Phys 109(7):074906–074907

    Article  Google Scholar 

  26. Yang J, Dunatunga S, Daraio C (2012) Amplitude-dependent attenuation of compressive waves in curved granular crystals constrained by elastic guides. Acta Mechanica 223(3):549–562

    Article  Google Scholar 

  27. Yang J, Silvestro C, Khatri D, De Nardo L, Daraio C (2011) Interaction of highly nonlinear solitary waves with linear elastic media. Physical Review E 83:046606

    Google Scholar 

  28. Johnson KL (1985) Contact mechanics. Cambridge University Press.

  29. Porter MADC, Szelengowicz I, Herbold EB, Kevrekidis PG (2009) Highly Nonlinear Solitary Waves in Heterogeneous Periodic Granular Media. Physica D 238:666–676

    Article  MATH  Google Scholar 

  30. Porter MA, Daraio C, Herbold EB, Szelengowicz I, Kevrekidis PG (2008) Highly nonlinear solitary waves in periodic dimer granular chains. Physical Review E 77:015601

    Article  Google Scholar 

  31. Jayaprakash KR, Starosvetsky Y, Vakakis AF (2011) New family of solitary waves in granular dimer chains with no precompression. Physical Review E 83(3):036606

    Article  MathSciNet  Google Scholar 

  32. Brillouin L (1953) Wave Propagation in Periodic Structures. Dover, New York

    MATH  Google Scholar 

  33. Phani AS, Fleck NA (2008) Elastic boundary layers in two-dimensional isotropic lattices. J Appl Mech 75(2):021020–021028

    Article  Google Scholar 

  34. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65

    Article  Google Scholar 

  35. Tsuji Y, Tanaka T, Ishida T (1992) Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe. Powder Technol 71(3):239–250

    Article  Google Scholar 

  36. Gere JM, Timoshenko SP (1997) Mechanics of materials, Pws Pub Co.

  37. Carretero-González R, Khatri D, Porter MA, Kevrekidis PG, Daraio C (2009) Dissipative solitary waves in granular crystals. Phys Rev Lett 102(2):024102

    Article  Google Scholar 

  38. Lamb GL (1980) Elements of soliton theory, John Wiley & Sons Inc.

  39. Scott A (2003) Nonlinear science: emergence and dynamics of coherent structures, Oxford University Press.

  40. Dauxois T, Peyrard M (2006) Physics of solitons, Cambridge University Press

  41. Daraio C, Nesterenko VF, Herbold EB, Jin S (2006) Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals. Phys Rev E 73(2):026610

    Article  Google Scholar 

  42. Job S, Melo F, Sokolow A, Sen S (2007) Solitary wave trains in granular chains: experiments, theory and simulations. Granul Matter 10:13–20

    Article  MATH  Google Scholar 

Download references

Acknowledgements

We acknowledge support from DARPA (Contract N. HR0011-10-C-0089, Dr. Jinendra Ranka), the National Science Foundation, Grant Number CMMI-0844540 (Career), and the Army Research Office (MURI grant US ARO W911NF-09-1-0436, Dr. David Stepp).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chiara Daraio.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, J., Daraio, C. Frequency- and Amplitude-Dependent Transmission of Stress Waves in Curved One-Dimensional Granular Crystals Composed of Diatomic Particles. Exp Mech 53, 469–483 (2013). https://doi.org/10.1007/s11340-012-9652-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-012-9652-y

Keywords

Navigation