Skip to main content
SpringerLink
Log in

Strain Variation with Doppler Shifts on the Free Surface of an Elastic Body

  • Published:
Physical Mesomechanics Aims and scope Submit manuscript

Abstract

The paper considers the problem of elastic wave reflection from a free surface moving with a constant velocity. Analytical expressions in the approximation of geometrical acoustics are derived for the frequency shifts, angles of reflection, and reflection coefficients of P, SV, and SH waves to estimate the strain state at the free surface. Based on respective calculations, the reflection coefficients and strain amplitudes at the free surface are analyzed as against each other and against the wave incidence angle, surface velocity, and elastic material parameters. The strain variation due to the motion of a free boundary is compared with frequency shifts.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

REFERENCES

  1. Surface Layers and Internal Interfaces in Heterogeneous Materials, V.E. Panin, Ed., Novosibirsk: SB RAS, 2006.

  2. Sarafanov, G.F. and Perevezentsev, V.N., Influence of the Free Surface and the Plastically Deformed Zone Size on the Screening of the Disclination Elastic Field, Tech. Phys. Lett., 2006, vol. 32, pp. 795–798.

  3. Wang, F., Zhao, J., Huang, P., Schneider, A.S., Lu, T.J., and Xu, K.W., Effects of Free Surface and Heterogeneous Residual Internal Stress on Stress-Driven Grain Growth in Nanocrystalline Metals, J. Nanomater., 2013, Article ID 934986. doi 10.1155/2013/ 934986

  4. Balokhonov, R.R., Romanova, V.A., Panin, A.V., Kazachenok, M.S., and Martynov, S.A., Strain Localization in Titanium with a Modified Surface Layer, Phys. Mesomech., 2018, vol. 21, no. 1, pp. 32–42.

  5. Tsukanov, A.A. and Psakhie, S.G., From the Soft Matter–Hard Matter Interface to Bio-Self-Organization and Hybrid Systems, Phys. Mesomech., 2017, vol. 20, no. 1, pp. 43–54. doi 10.1134/S1029959917010040

  6. Brekhovskikh, L.M. and Godin, O.A., Acoustics of Layered Media, Springer-Verlag, 1990.

  7. Singh, B., Reflection of P and SV Waves from Free Surface of an Elastic Solid with Generalized Thermodifusion, J. Earth Syst. Sci., 2005, vol. 114, no. 2, pp. 159–168.

  8. Ciarletta, M. and Sumbatyan, M.A., Reflection of Plane Waves by the Free Boundary of a Porous Elastic Half-Space, J. Sound. Vib., 2003, vol. 259, no. 2, pp. 253–264.

  9. Chertova, N.V., The Character of Deformations on the Free Surface of an Elastic Body, Tech. Phys. Lett., 2015, vol. 41, pp. 1075–1078.

  10. Chertova, N.V. and Grinyaev, Yu.V., Deformation Features on the Free Surface and Rigid Interface during Elastic Wave Reflection, Phys. Mesomech., 2018, vol. 21, no. 3, pp. 208–215.

  11. Einstein, A., Zur Elektrodynamik bewegter Körper, Ann. Phys., Leipzig, 1905, vol. 322, no. 10, pp. 891–921.

  12. Eden, A., The Search for Christian Doppler, Wien: Springer-Verlag, 1992.

  13. Schuster, P.M., Moving the Stars: Christian Doppler, His Life, His Works and Principle and the World After, Pöllauberg: Living Edition Publishers, 2005.

  14. Li, G., Zentgraf, T., and Zhang, S., Doppler Effect in Nonlinear Optics, Nat. Phys., 2016, vol. 12, pp. 736–740. doi 10.1038/nphys3699

  15. Rozanov, N.N., Superluminal Parametric Doppler Effect in Dielectrics and in an Electron-Positron Vacuum, JETP Lett., 2012, vol 95, no. 12, pp. 609–612.

  16. Korech, O., Steinitz, U., Gordon, R.J., Averbukh, I.Sh., and Prior, Y., Observing Molecular Spinning via the Rotational Doppler Effect, Nat. Photon., 2013, vol. 7, pp. 711–714. doi 10.1038/nphoton.2013.189

  17. Watanabe, K., Elastodynamic Doppler Effects by a Moving Stress-Free Edge, Int. J. Eng. Sci., 2010, vol. 48, no. 22, pp. 1995–2014.

  18. Kolsky, H., Stress Waves in Solids, Oxford: Clarendon, 1953.

Download references

Funding

The work was performed under Fundamental Research Program of the State Academies of Sciences for 2013–2020.

Author information

Authors and Affiliations

  1. Institute of Strength Physics and Materials Science, Siberian Branch, Russian Academy of Sciences, 634055, Tomsk, Russia

    N. V. Chertova & Yu. V. Grinyaev

Authors
  1. N. V. Chertova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu. V. Grinyaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. V. Chertova.

Additional information

Russian Text © The Author(s), 2019, published in Fizicheskaya Mezomekhanika, 2019, Vol. 22, No. 2, pp. 77–85.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chertova, N.V., Grinyaev, Y. . Strain Variation with Doppler Shifts on the Free Surface of an Elastic Body. Phys Mesomech 23, 205–212 (2020). https://doi.org/10.1134/S1029959920030042

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1029959920030042

Keywords

Search

Navigation