The in-situ measurement of thermal stress in slender beams, or long continuous welded rails, may prevent structural anomalies. With this aim, we investigated the coupling dynamics between a beam and the highly nonlinear solitary waves propagating along a straight granular chain in contact with the beam. We hypothesized that these waves can be used to measure the stress of thermally loaded structures, or to infer the neutral temperature, i.e., the temperature at which this stress is null. We studied numerically and experimentally the mechanical interaction of one and two straight chains of spherical particles in contact with a prismatic beam that is subjected to heat. The results show that certain features of the waves are affected by the beam’s stress. In the future, these findings may be used to develop a novel nondestructive evaluation technique for the prediction of neutral temperature and thermal buckling.
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Bartoli, I., Phillips, R., Coccia, S., Srivastava, A., Lanza di Scalea, F., Fateh, M., Carr, G.: Stress dependence of ultrasonic guided waves in rails. Transp. Res. Rec. 2159, 91–97 (2010)
Carretero-González, R., Khatri, D., Porter, M.A., Kevrekidis, P.G., Daraio, C.: Dissipative solitary waves in granular crystals. Phys. Rev. Lett. 102(2), 024102 (2009)
Coste, C., Falcon, E., Fauve, S.: Solitary waves in a chain of beads under Hertz contact. Phys. Rev. E. 56(5), 6104–6117 (1997)
Daraio, C., Nesterenko, V.F., Herbold, E.B., Jin, S.: Strongly nonlinear waves in a chain of Teflon beads. Phys. Rev. E. 72(1), 016603 (2005)
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 (2006)
Job, S., Melo, F., Sokolow, A., Sen, S.: How Hertzian solitary waves interact with boundaries in a 1D granular medium. Phys. Rev. Lett. 94(17), 178002 (2005)
Job, S., Melo, F., Sokolow, A., Sen, S.: Solitary wave trains in granular chains: experiments, theory and simulations. Granul. Matter 10(1), 13–20 (2007)
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)
Nesterenko, V.F.: Propagation of nonlinear compression pulses in granular media. J. Appl. Mech. Tech. Phys. 24(5), 733–743 (1983)
Nesterenko, V.F.: Dynamics of Heterogeneous Materials. Springer, New York (2001)
Nesterenko, V.F., Lazaridi, A.N., Sibiryakov, E.B.: The decay of soliton at the contact of two “acoustic vacuums”. J. Appl. Mech. Tech. Phys. 36(2), 166–168 (1995)
Yang, J., Silvestro, C., Khatri, D., De Nardo, L., Daraio, C.: Interaction of highly nonlinear solitary waves with linear elastic media. Phys. Rev. E. 83(4), 046606 (2011)
Boechler, N., Theocharis, G., Daraio, C.: Bifurcation-based acoustic switching and rectification. Nat. Mater. 10(9), 665–668 (2011)
Donahue, C.M., Anzel, P.W., Bonanomi, L., Keller, T.A., Daraio, C.: Experimental realization of a nonlinear acoustic lens with a tunable focus. Appl. Phys. Lett. 104(1), 014103 (2014)
Fraternali, F., Porter, M.A., Daraio, C.: Optimal design of composite granular protectors. Mech. Adv. Mater. Struct. 17(1), 1–19 (2009)
Li, F., Zhao, L., Tian, Z., Yu, L., Yang, J.: Visualization of solitary waves via laser Doppler vibrometry for heavy impurity identification in a granular chain. Smart Mater. Struct. 22(3), 035016 (2013a)
Li, F., Yu, L., Yang, J.: Solitary wave-based strain measurements in one-dimensional granular crystals. J. Phys. D Appl. Phys. 46(15), 155106 (2013b)
Shelke, A., Uddin, A., Yang, J.: Impact identification in sandwich structures using solitary wave-supporting granular crystal sensors. AIAA J. 52(10), 2283–2290 (2014)
Spadoni, A., Daraio, C.: Generation and control of sound bullets with a nonlinear acoustic lens. Proc. Natl. Acad. Sci. U.S. 107(16), 7230–7234 (2010)
Ni, X., Rizzo, P., Yang, J., Katri, D., Daraio, C.: Monitoring the hydration of cement using highly nonlinear solitary waves. NDT E Int. 52, 76–85 (2012)
Ni, X., Rizzo, P.: Highly nonlinear solitary waves for the inspection of adhesive joints. Exp. Mech. 52(9), 1493–1501 (2012a)
Ni, X., Rizzo, P.: Use of highly nonlinear solitary waves in nondestructive testing. Mater. Eval. 70(5), 561–569 (2012b)
Yang, J., Khatri, D., Anzel, P., Daraio, C.: Interaction of highly nonlinear solitary waves with thin plates. Int. J. Solids Struct. 49(13), 1463–1471 (2012a)
Yang, J., Silvestro, C., Sangiorgio, S.N., Borkowski, S.L., Ebramzadeh, E., De Nardo, L., Daraio, C.: Nondestructive evaluation of orthopaedic implant stability in THA using highly nonlinear solitary waves. Smart Mater. Struct. 21(1), 012002 (2012b)
Cai, L., Rizzo, P., Al-Nazer, L.: On the coupling mechanism between nonlinear solitary waves and slender beams. Int. J. Solids Struct. 50(25), 4173–4183 (2013)
Tedesco, J.W., McDougal, W.G., Ross, C.A.: Structural dynamics: theory and applications. Addison-Wesley, Montlo Park, CA (1999)
Lanza di Scalea, F., Rizzo, P., Seible, F.: Stress measurement and defect detection in steel strands by guided stress waves. J. Mater. Civ. Eng. 15(3), 219–227 (2003)
Rizzo, P., Lanza di Scalea, F.: Effect of frequency on the acoustoelastic response of steel bars. Exp. Tech. 27(6), 40–43 (2003)
Rizzo, P., Lanza di Scalea, F.: Monitoring in cable stays via guided wave magnetostrictive ultrasonics. Mater. Eval. 62, 1057–1065 (2004)
Szelengowicz, I., Kevrekidis, P.G., Daraio, C.: Wave propagation in square granular crystals with spherical interstitial intruders. Phys. Rev. E 86(6), 061306 (2012)
Job, S., Santibanez, F., Tapia, F., Melo, F.: Wave localization in strongly nonlinear Hertzian chains with mass defect. Phys. Rev. E 80(2), 025602 (2009)
Hascoët, E., Herrmann, H.J.: Shocks in non-loaded bead chains with impurities. Eur. Phys. J. B 14(1), 183–190 (2000)
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)
Tichler, A.M., Gómez, L.R., Upadhyaya, N., Campman, X., Nesterenko, V.F., Vitelli, V.: Transmission and reflection of strongly nonlinear solitary waves at granular interfaces. Phys. Rev. Lett. 111(4), 048001 (2013)
Yang, J., Gonzalez, M., Kim, E., Agbasi, C., Sutton, M.: Attenuation of solitary waves and localization of breathers in 1D granular crystals Visualized via High Speed Photography. Exp. Mech. 54(6), 1043–1057 (2014)
This project was supported by the U.S. Federal Railroad Administration under contract DTFR53-12-C-00014. Partial support came from the U.S. National Science Foundation grant CMMI 1200259. We thank Mr. Charles “Scooter” Hager for helping in the design and construction of the house-built steel frame.
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Bagheri, A., Ribolla, E.L.M., Rizzo, P. et al. On the coupling dynamics between thermally stressed beams and granular chains. Arch Appl Mech 86, 541–556 (2016). https://doi.org/10.1007/s00419-015-1039-y
- Highly nonlinear solitary waves
- Nondestructive testing
- Thermal stress
- Granular chains
- Neutral temperature
- Discrete particle model