Effect of Radial Confinement on Wave Propagation and Vibrational Response in Bars

  • Jacob C. DodsonEmail author
  • Jason R. Foley
  • Janet C. Wolfson
  • Jonathan Hong
  • Vincent Luk
  • Alain Beliveau
  • Alexander Idesman
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


It is currently beyond the state-of-the art to accurately predict the instantaneous dynamic response of a structure with rapidly changing boundary conditions. In order to establish a basic understanding of changing boundary conditions, we examine the wave propagation through a bar subject to mechanical confinement. The Air Force Research Laboratory has conducted several experiments investigating the effect of non-traditional boundary conditions, such as mid-structure confinement, on the local and global dynamic response of rods using a modified Hopkinson Bar configuration with radial clamping. We have shown that the wave velocity in the mechanically clamped area is significantly lower than that in a stress free bar. This paper presents the experimental results and analytical modeling of the effect of radial confinement on dynamic response in bars.


Wave propagation Confined effects Hopkinson bar Dispersion Experimental mechanics 



The authors would like to thank AFOSR (Program Manager: Dr. David Stargel) and the Air Force Research Laboratory for supporting this research effort. Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the United States Air Force.


  1. 1.
    Pochhammer L (1876) On the propagation velocities of small oscillations in an unlimited isotropic circular cylinder. J fur die Reine Angew Mathematik 81:324–326Google Scholar
  2. 2.
    Chree C (1889) The equations of an isotropic elastic solid in polar and cylindrical coordinates, their solutions and applications. Trans Camb Philos Soc 14:250–369Google Scholar
  3. 3.
    Kolsky H (1963) Stress waves in solid. Clarendon Press, OxfordGoogle Scholar
  4. 4.
    Ueda K, Umeda A (1998) Dynamic response of strain gages up to 300 kHz. Exp Mech 38(2):93–98CrossRefGoogle Scholar
  5. 5.
    2001, Kulite Strain Gage Manual, Kulite Semiconductor ProductsGoogle Scholar
  6. 6.
    Prescale Pressure Sensitive Film, 6 Oct 2014,
  7. 7.
    2009, Precision 28144 quad-channel wideband transducer conditioner with voltage and current excitation (datasheet). Precision Filters, IthacaGoogle Scholar
  8. 8.
    2003, NI PXI-6133 Specifications, National Instruments, AustinGoogle Scholar
  9. 9.
    Idesman AV, Mates SP (2014) Accurate finite element simulation and experimental study of elastic wave propagation in a long cylinder under impact loading. Int J Impact Eng 71:1–16CrossRefGoogle Scholar
  10. 10.
    Idesman AV (2011) Accurate time integration of linear elastodynamics problems. Comput Models Eng Sci 71(2):111e48MathSciNetGoogle Scholar
  11. 11.
    Van Zandt T (2006) Development of efficient reduced models for multi-body dynamics simulations of helicopter wing missile configurations. Master’s thesis, University of Massachusetts LowellGoogle Scholar
  12. 12.
    Dodson J, Inman D (2014) Investigating thermally induced acoustoelastic effect in isotropic media with lamb wave. J Acoust Soc Am 136:2532–2543CrossRefGoogle Scholar
  13. 13.
    Doyle JF (1997) Wave propagation in structures: spectral analysis using fast discrete fourier transforms. Springer, New YorkCrossRefzbMATHGoogle Scholar
  14. 14.
    Follansbee P, Frantz C (1983) Wave propagation in the split Hopkinson pressure bar. J Eng Mater Technol 105(1):61–66CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2015

Authors and Affiliations

  • Jacob C. Dodson
    • 1
    Email author
  • Jason R. Foley
    • 1
  • Janet C. Wolfson
    • 1
  • Jonathan Hong
    • 2
  • Vincent Luk
    • 2
  • Alain Beliveau
    • 2
  • Alexander Idesman
    • 3
  1. 1.Air Force Research Laboratory/RWMFValparaisoUSA
  2. 2.Applied Research AssociatesValparasioUSA
  3. 3.Texas Tech UniversityLubbockUSA

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