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On the Use of L-shaped Granular Chains for the Assessment of Thermal Stress in Slender Structures

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Abstract

Slender beams subjected to compressive load are common in civil engineering. The rapid in-situ measurement of this stress may help preventing structural anomalies. In this article, we describe the coupling mechanism between highly nonlinear solitary waves (HNSWs) propagating along an L-shaped granular system and a beam in contact with the granular medium. We evaluate the use of these waves to measure stress in thermally loaded structures and to estimate the neutral temperature, i.e. the temperature at which the stress is null. We investigate numerically and experimentally one and two L-shaped chains of spherical particles in contact with a prismatic beam subjected to heat. We find that certain features of the solitary waves are affected by the beam’s stress. In the future these findings may be used to develop a novel sensing system for the nondestructive prediction of neutral temperature and thermal buckling.

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References

  1. Bartoli I, Phillips R, Coccia S, Srivastava A, Lanza di Scalea F, Fateh M, Carr G (2010) Stress dependence of ultrasonic guided waves in rails. Transp Res Rec 2159:91–97

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Nesterenko VF, Lazaridi AN, Sibiryakov EB (1995) The decay of soliton at the contact of two “acoustic vacuums”. J Appl Mech Tech Phys 36:166–168

    Article  Google Scholar 

  4. Nesterenko VF (2001) Dynamics of heterogeneous materials. Springer, New York

    Book  Google Scholar 

  5. Lazaridi AN, Nesterenko VF (1985) Observation of a new type of solitary waves in one-dimensional granular medium. J Appl Mech Tech Phys 26:405–408

    Article  Google Scholar 

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

    Article  Google Scholar 

  7. Daraio C, Nesterenko VF, Herbold EB, Jin S (2005) Strongly nonlinear waves in a chain of Teflon beads. Phys Rev E 72:016603-1–016603-9

    Article  Google Scholar 

  8. Daraio C, Nesterenko VF, Herbold EB, Jin S (2006) Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals. Phys Rev E 73:026610-1–026610-10

    Google Scholar 

  9. Job S, Melo F, Sokolow A, Sen S (2005) How Hertzian solitary waves interact with boundaries in a 1D granular medium. Phys Rev Lett 94:178002-1–178002-4

    Article  Google Scholar 

  10. 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 

  11. Carretero-González R, Khatri D, Porter MA, Kevrekidis PG, Daraio C (2009) Dissipative solitary waves in granular crystals. Phys Rev Lett 102:024102-1–024102-4

    Article  Google Scholar 

  12. Yang J, Silvestro C, Khatri D, De Nardo L, Daraio C (2011) Interaction of highly nonlinear solitary waves with linear elastic media. Phys Rev E 83:046606-1–046606-12

    Google Scholar 

  13. Yang J, Khatri D, Anzel P, Daraio C (2012) Interaction of highly nonlinear solitary waves with thin plates. Int J Solids Struct 49:1463–1471

    Article  Google Scholar 

  14. Yang J, Silvestro C, Sangiorgio SN, Borkowski SL, Ebramzadeh E, De Nardo L, Daraio C (2012) Nondestructive evaluation of orthopaedic implant stability in THA using highly nonlinear solitary waves. Smart Mater Struct 21:012002-1–012002-10

    Google Scholar 

  15. Ni X, Rizzo P, Yang J, Katri D, Daraio C (2012) Monitoring the hydration of cement using highly nonlinear solitary waves. NDT&E Int 52:76–85

    Article  Google Scholar 

  16. Ni X, Rizzo P (2012) Highly nonlinear solitary waves for the inspection of adhesive joints. Exp Mech 52:1493–1501

    Article  Google Scholar 

  17. Ni X, Rizzo P (2012) Use of highly nonlinear solitary waves in NDT. Mater Eval 70:561–569

    Google Scholar 

  18. Cai L, Rizzo P, Al-Nazer L (2013) On the coupling mechanism between nonlinear solitary waves and slender beams. Int J Solids Struct 50:4173–4183

    Article  Google Scholar 

  19. Hascoët E, Herrmann HJ (2000) Shocks in non-loaded bead chains with impurities. Eur Phys J B 14(1):183–190

    Article  Google Scholar 

  20. Job S, Santibanez F, Tapia F, Melo F (2009) Wave localization in strongly nonlinear Hertzian chains with mass defect. Phys Rev E 80(2):025602

    Article  Google Scholar 

  21. Theocharis G, Kavousanakis M, Kevrekidis PG, Daraio C, Porter MA, Kevrekidis IG (2009) Localized breathing modes in granular crystals with defects. Phys Rev E 80(6):066601

    Article  Google Scholar 

  22. Szelengowicz I, Kevrekidis PG, Daraio C (2012) Wave propagation in square granular crystals with spherical interstitial intruders. Phys Rev E 86(6):061306

    Article  Google Scholar 

  23. Li F, Zhao L, Tian Z, Yu L, Yang J (2013) Visualization of solitary waves via laser Doppler vibrometry for heavy impurity identification in a granular chain. Smart Mater Struct 22(3):035016

    Article  Google Scholar 

  24. Li F, Yu L, Yang J (2013) Solitary wave-based strain measurements in one-dimensional granular crystals. J Phys D Appl Phys 46(15):155106

    Article  Google Scholar 

  25. Tichler AM, Gómez LR, Upadhyaya N, Campman X, Nesterenko VF, Vitelli V (2013) Transmission and reflection of strongly nonlinear solitary waves at granular interfaces. Phys Rev Lett 111(4):048001

    Article  Google Scholar 

  26. Yang J, Gonzalez M, Kim E, Agbasi C, Sutton M (2014) Attenuation of Solitary Waves and Localization of Breathers in 1D Granular Crystals Visualized via High Speed Photography. Exp Mech 1–15

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

    Article  MATH  Google Scholar 

  28. Tedesco JW, McDougal WG, Ross CA (1999) Structural dynamics: theory and applications. Addison-Wesley, Montlo Park

    Google Scholar 

  29. Cai L, Yang J, Rizzo P, Ni X, Daraio C (2013) Propagation of highly nonlinear solitary waves in a curved granular chain. Granul Matter 15(3):357–366

    Article  Google Scholar 

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Acknowledgments

This project was supported by the U.S. Federal Railroad Administration under contract DTFR53-12-C-00014. We thank Mr. Charles “Scooter” Hager for helping in the design and construction of the house-built steel frame.

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Authors and Affiliations

  1. Laboratory for Nondestructive Evaluation and Structural Health Monitoring Studies, Department of Civil and Environmental Engineering, University of Pittsburgh, 3700 O’Hara Street, Pittsburgh, PA, 15261, USA

    A. Bagheri & P. Rizzo

  2. Department of Civil, Environmental, Aerospace, and Materials Engineering, University of Palermo, Viale delle Scienze, Ed. 8, Palermo, 90128, Italy

    E. La Malfa Ribolla & G. Giambanco

  3. Office of Research and Development, Federal Railroad Administration, 1200 New Jersey Avenue, SE, Washington, DC, 20590, USA

    L. Al-Nazer

Authors
  1. A. Bagheri
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  2. E. La Malfa Ribolla
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  3. P. Rizzo
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  4. L. Al-Nazer
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  5. G. Giambanco
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Correspondence to P. Rizzo.

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Bagheri, A., La Malfa Ribolla, E., Rizzo, P. et al. On the Use of L-shaped Granular Chains for the Assessment of Thermal Stress in Slender Structures. Exp Mech 55, 543–558 (2015). https://doi.org/10.1007/s11340-014-9964-1

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  • DOI: https://doi.org/10.1007/s11340-014-9964-1

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