Skip to main content
Log in

Reflection of a decaying traveling wave from a notch in a bar

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

We study the reflection from a transverse notch and the propagation of a longitudinal decaying traveling wave in a bar by using the simplest model of the stress-strain state in the notch region and obtain the solution dependence on the notch parameters. The solution of the inverse problem permits determining the notch coordinate and the parameter determining its depth and length from the data describing the incident and reflected waves at the observation site.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. B. V. Sidorov and S. A. Martynov, “Recommended Technology of Diagnostics of Buried Pipelines,” Kontrol’. Diagnostika, No. 12, 18–19 (2005)

  2. Yu. V. Van’kov, R. B. Kazakov, and E. R. Yakovleva, “Natural Frequencies as Diagnostic Criteria for Flaw Detection,” Electronic J. “Technical Acoustics,” http://ejta.org, 2003, 5.

  3. M. A. Il’gamov, “Diagnostics of Damage of a Vertical Rod,” Trudy Inst. Mekh. UNTs RAN, No. 5, 201–211 (2007).

  4. G. Biscontin, A. Morassi, and P. Wendel, “Asymptotic Separation of Spectrum in Notched Rods,” J. Vib. Contr. 4(3), 237–251 (1998).

    Article  Google Scholar 

  5. G. M. L. Gladwell, Inverse Problems in Vibration (Kluwer, Dordrecht, 2004; NITs “Regular. Khaotich. Din.,” Moscow-Izhevsk, 2008).

    Google Scholar 

  6. T. Pritz, “Apparent Complex Young’s Modulus of a Longitudinally Vibrating Viscoelastic Rod,” J. Sound Vibr. 77(1), 93–100 (1981).

    Article  ADS  Google Scholar 

  7. D. Benatar, D. Rittel, and A. L. Yarin, “Theoretical and Experimental Analysis of Longitudinal Wave Propagation in Cylindrical Viscoelastic Rods,” J. Mech. Phys. Solids 51(8), 1413–1431 (2003).

    Article  ADS  MATH  Google Scholar 

  8. S. L. Lopatnikov, B. A. Gama, K. Krauthouser, and G. Gillespie, “Applicability of the Classical Analysis of Experiments with Split Hopkins Pressure Bar,” Pis’ma Zh. Techn. Fiz. 30(3), 39–46 (2004) [Tech. Phys. Lett. (Engl. Transl.) 30 (2), 102–105 (2004)].

    Google Scholar 

  9. H. Kolsky, “An Investigation of Mechanical Properties of Materials at Very High Rates of Loading,” Proc. Phys. Soc. London. Ser. B 62(359), 676–700 (1949).

    Article  ADS  Google Scholar 

  10. V. V. Meleshko, A. A. Bondarenko, S. A. Dovgii, et al., “Elastic Waveguides: History and the Present,” Mat. Metody Fiz.-Mekh. Polya 51(2), 86–104 (2008).

    MATH  Google Scholar 

  11. A. O. Vatul’yan, Inverse Problems in Mechanics of a Deformable Solid (Fizmatlit, Moscow, 2007) [in Russian].

    Google Scholar 

  12. A. O. Vatul’yan and N. O. Soluyanov, “Determining the Location and Dimensions of a Cavity in an Elastic Rod,” Defectoskop. 41(9), 44–56 (2005) [Russ. J. Nondestruct. Test. (Engl. Transl.) 41 (9), 586–593 (2005)].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. G. Khakimov.

Additional information

Original Russian Text © M.A. Il’gamov, A.G. Khakimov, 2011, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2011, No. 4, pp. 116–125.

About this article

Cite this article

Il’gamov, M.A., Khakimov, A.G. Reflection of a decaying traveling wave from a notch in a bar. Mech. Solids 46, 589–596 (2011). https://doi.org/10.3103/S0025654411040091

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654411040091

Keywords

Navigation