Dispersion correction in split-Hopkinson pressure bar: theoretical and experimental analysis

  • Anatolii Mikhailovich BragovEmail author
  • Andrei Kirillovich Lomunov
  • Dmitrii Aleksandrovich Lamzin
  • Aleksandr Yurevich Konstantinov
Original Article


The paper presents experimental and mathematical analysis of the dispersion effect of pulses, which propagate along an elastic bar whose cross section has a finite radius. In some cases, dispersion can influence significantly the interpretation of the experimental data, obtained in experimental schemes, which are based on using measuring bars for investigation material behavior at high strain rates (the split-Hopkinson pressure bar method and its modifications). Solutions for the Pochhammer–Chree equation are obtained for various measuring bars used in experimental setups in the Research Institute for Mechanics of Lobachevsky State University of Nizhny Novgorod. The procedure of pulse shift accounting for dispersion has been implemented and tested on the basis of our experimental data and the data available in the existing scientific literature. This procedure was employed to analyze the influence of pulse shape on the degree of its change in shape during its propagation along a measuring bar. It is shown how the procedure of dispersion shift improves the quality of interpretation of primary experimental data for some materials.


The Kolsky method Measuring bar Dispersion Wave number Experiment Deformation Frequency Frequency equation Strain pulse 


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The theoretical part of work was carried out by a Grant from the Russian Science Foundation (Project No. 17-79-20161). The experimental part of work was done in the frame of the state task of the Ministry of Education and Science of the Russian Federation No. 9.6109.2017/6.7.


  1. 1.
    Kolsky, H.: An investigation of the mechanical properties of materials at very high rates of loading. Proc. Phys. Soc. Lond. Sect. B 62, 676–700 (1949)ADSCrossRefGoogle Scholar
  2. 2.
    Engelbrecht, J., Berezovski, A.: Reflections on mathematical models of deformation waves in elastic microstructured solids. Math. Mech. Complex Syst. 3(1), 43–82 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Altenbach, H., Eremeyev, V.A., Lebedev, L.P., Rendón, L.A.: Acceleration waves and ellipticity in thermoelastic micropolar media. Arch. Appl. Mech. 80(3), 217–227 (2010)ADSCrossRefzbMATHGoogle Scholar
  4. 4.
    Rosi, G., Placidi, L., Nguyen, V.H., Naili, S.: Wave propagation across a finite heterogeneous interphase modeled as an interface with material properties. Mech. Res. Commun. 84, 43–48 (2017)CrossRefGoogle Scholar
  5. 5.
    dell’Isola, F., Madeo, A., Placidi, L.: Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua. Z. Angew. Math. Mech. 92(1), 52–71 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Davies, R.M.: A critical study of the Hopkinson pressure bar. Philos. Trans. R. Soc. Lond. Ser. A 240(821), 375–457 (1948)ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    Follansbee, P.S., Frantz, C.: Wave propagation in the split Hopkinson pressure bar. ASME J. Eng. Mater. Technol. 105, 61–66 (1983)CrossRefGoogle Scholar
  8. 8.
    Gong, J.C., Malvern, L.E., Jenkins, D.A.: Dispersion investigation in the split Hopkinson pressure bar. ASME J. Eng. Mater. Technol. 112, 309–314 (1990)CrossRefGoogle Scholar
  9. 9.
    Lifshitz, J.M., Leber, H.: Data processing in the split Hopkinson pressure bar tests. Int. J. Impact Eng. 15(6), 723–733 (1994)CrossRefGoogle Scholar
  10. 10.
    Bragov, A.M., Konstantinov, A.Y., Medvedkina, M.V.: Wave dispersion in split Hopkinson pressure bars in dynamic testing of brittle materials. Vestn. Lobachevsky Univ. Nizhni Novgorod 6(1), 158–162 (2011). ISSN: 1993-1778Google Scholar
  11. 11.
    Pochhammer, L.: Uber Fortplanzungsgeschwindigkeiten kleiner Schwingungen in einem unbergrenzten isotropen Kreiszylinder. J. Reine Angew. Math. 81, 324 (1876). (German)MathSciNetGoogle Scholar
  12. 12.
    Bancroft, D.: The velocity of longitudinal wave in cylindrical bars. Phys. Rev. 59, 588–593 (1941)ADSCrossRefGoogle Scholar
  13. 13.
    Le, K.C.: Vibrations of Shells and Rods. Springer, Berlin (1999)CrossRefzbMATHGoogle Scholar
  14. 14.
    Yew, E.H., Chen, C.S.: Experimental study of dispersive waves in beam and rod using FFT. ASME J. Appl. Mech. 45, 375–457 (1978)CrossRefGoogle Scholar
  15. 15.
    Gorham, D.: A numerical method for the correction of dispersion in pressure bar signals. J. Phys. E Sci. Instrum. 16, 477–479 (1983)ADSCrossRefGoogle Scholar
  16. 16.
    Follansbee, P., Frantz, C.: Wave propagation in the split Hopkinson pressure bar. J. Eng. Mater. Technol. 105, 61–66 (1983)CrossRefGoogle Scholar
  17. 17.
    Rigby, S.E., Barr, A.D., Clayton, M.: A review of Pochhammer–Chree dispersion in the Hopkinson bar. Proc. Inst. Civ. Eng. Eng. Comput. Mech. 171(1), 3–13 (2018). Google Scholar
  18. 18.
    Lee, C., Crawford, R.: A new method for analysing dispersed bar gauge data. Meas. Sci. Technol. 4, 931–937 (1993)ADSCrossRefGoogle Scholar
  19. 19.
    Lee, C., Crawford, R., Mann, K., Coleman, P., Petersen, C.: Evidence of higher Pochhammer–Chree modes in an unsplit Hopkinson bar. Meas. Sci. Technol. 6, 853–859 (1995)ADSCrossRefGoogle Scholar
  20. 20.
    Puckett, A.: An experimental and theoretical investigation of axially symmetric wave propagation in thick cylindrical waveguides. PhD thesis, The Graduate School, The Unversity of Maine, USA (2004)Google Scholar
  21. 21.
    Husemeyer, P.: Theoretical and numerical investigation of multiple-mode dispersion in Hopkinson bars. PhD thesis, Blast Impact and Survivability Research Unit, Department of Mechanical Engineering, University of Cape Town, South Africa (2011)Google Scholar
  22. 22.
    Gama, B.A., Lopatnikov, S.L., Gillespie Jr., J.W.: Hopkinson bar experimental technique: a critical review. Appl. Mech. Rev. (2004). Google Scholar
  23. 23.
    Li, Z., Lambros, J.: Determination of the dynamic response of brittle composites by the use of split Hopkinson pressure bar. Compos. Sci. Technol. 59, 1097–1107 (1999)CrossRefGoogle Scholar
  24. 24.
    Klepaczko, J.: Advanced experimental techniques in material testing. In: Nowacki, W.K., Klepachko, J.R. (eds.) New Experimental Methods in Material Dynamics and Impact. Trends in Mechanics of Materials, pp. 1–58. Institute of Fundamental Technological Research Polish Academy of Sciences, Warsaw (2001)Google Scholar
  25. 25.
    Bacon, C.: An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar. Exp. Mech. 38, 242 (1998). CrossRefGoogle Scholar
  26. 26.
    Ramirez, H., Rubio-Gonzalez, C.: Finite-element simulation of wave propagation and dispersion in Hopkinson bar test. Mater. Des. 27, 36–44 (2006)CrossRefGoogle Scholar
  27. 27.
    Le, K.C.: High-frequency longitudinal vibrations of elastic rods. J. Appl. Math. Mech. (PMM) 50, 335–341 (1986)ADSCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Research Institute for MechanicsNational Research Lobachevsky State University of Nizhny NovgorodNizhny NovgorodRussian Federation

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