Skip to main content
SpringerLink
Log in

Longitudinal Waves in Structurally Inhomogeneous Viscoelastic Solids with a Quadratic–Bimodular Nonlinearity Decreasing with Increasing Frequency

  • Published:
Radiophysics and Quantum Electronics Aims and scope

We study theoretically the propagation of longitudinal acoustic waves in structurally inhomogeneous viscoelastic solids with a quadratic–bimodular nonlinearity decreasing with increasing frequency. Exact solutions for stationary waves propagating without changing their shape are obtained. Analytical and numerical solutions for the evolution of an initially harmonic wave are presented, and the amplitude–frequency dependences of nonlinear effects in such media are revealed.

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

Similar content being viewed by others

References

  1. L. K. Zarembo and M. A. Krasil’nikov, Introduction to Nonlinear Acoustics [in Russian], Nauka, Moscow (1966).

  2. O.V.Rudenko and S. I. Soluyan, Theoretical Foundations of Nonlinear Acoustics, Plenum, New York (1977).

    Book  Google Scholar 

  3. L. K. Zarembo and M. A. Krasil’nikov, Sov. Phys. Usp., 13, No. 12, 778–797 (1970). https://doi.org/10.1070/PU1971v013n06ABEH004281

  4. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6, Fluid Mechanics, 2nd ed., Elsevier, Amsterdam, The Netherlands (2013).

  5. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Pergamon Press, Oxford (1959).

    Google Scholar 

  6. K. A. Naugol’nykh and L.A.Ostrovsky, Nonlinear Wave Processes in Acoustics, Cambridge University Press, Cambridge (1998).

  7. S. N. Gurbatov, O.V.Rudenko, and A. I. Saichev, Waves and Structures in Nonlinear Nondispersive Media, Springer (2011).

  8. R. T. Beyer, Nonlinear Acoustics in Fluids, Van Nostrand Reinhold, New York (1984).

    Google Scholar 

  9. M. F. Hamilton and D.T.Blackstock, Nonlinear Acoustics, Academic Press, New York (1988).

    Google Scholar 

  10. B. O. Enflo and C.M.Hedberg, Theory of Nonlinear Acoustics in Fluids, Kluwer Academic Publishers, New York (2004).

    Google Scholar 

  11. M. A. Isakovich, General Acoustics [in Russian], Nauka, Moscow (1973).

  12. V. E. Nazarov, L. A. Ostrovsky, I.A. Soustova, and A.M. Sutin, Phys. Earth Planet. Inter ., 50, No. 1, 65–73 (1988). https://doi.org/10.1016/0031-9201(88)90094-5

    Article  ADS  Google Scholar 

  13. R.A. Guyer and P.A. Johnson, Nonlinear Mesoscopic Elasticity: the Complex Behaviour of Granular Media Including Rocks and Soil, Wiley-VCH Verlag GmbH & Co. KgaA, Weinheim (2009).

  14. O.V.Rudenko, Phys. Usp., 49, No. 1, 69–87 (2006). https://doi.org/10.1070/PU2006v049n01ABEH005876

    Article  ADS  MathSciNet  Google Scholar 

  15. V. Nazarov and A. Radostin, Nonlinear Acoustic Waves in Microinhomogeneous Solids, John Wiley & Sons, Chichester (2015).

    Google Scholar 

  16. V.E. Nazarov and S. B.Kiyashko, Radiophys. Quantum Electron., 63, No. 1, 64–72 (2020). https://doi.org/10.1007/s11141-020-10035-x

    Article  ADS  Google Scholar 

  17. A. Granato and K. Luke, J. Appl. Phys., 27, 583–593 (1956). https://doi.org/10.1063/1.1722436

    Article  ADS  Google Scholar 

  18. S. Asano, J. Phys. Soc. Jap., 29, No. 4, 952–963 (1970). https://doi.org/10.1143/JPSJ.29.952

    Article  ADS  Google Scholar 

  19. Warren P. Mason, ed., Application to Quantum and Solid State Physics, in Physical Acoustics: Principles and Methods, Vol. 4, Part A, Academic Press, New York and London (1966).

  20. K. E. van den Abeele, P. A. Johnson, R.A.Guyer, and K.R. McCall, J. Acoust. Soc. Am., 101, 1885–1898 (1997). https://doi.org/10.1121/1.418198

    Article  ADS  Google Scholar 

  21. V. Gusev, J. Acoust. Soc. Am., 107, 3047–3058 (2000). https://doi.org/10.1121/1.429333

    Article  ADS  Google Scholar 

  22. V. Gusev, Ultrasonics, 44, e1335–e1338 (2006). https://doi.org/10.1016/j.ultras.2006.05.012

    Article  Google Scholar 

  23. V.E. Nazarov, A. V. Radostin, L.A.Ostrovsky, and I. A. Soustova, Acoust. Phys., 49, No. 3, 344–353 (2003) https://doi.org/10.1134/1.1574363

    Article  ADS  Google Scholar 

  24. Y. Li, O.Bou Matar, B. Li, and X. Chen, Wave Motion, 52, 54–65 (2015). https://doi.org/10.1016/j.wavemoti.2014.08.008

  25. D. Broda, W. J. Staszewski, A. Martowicz, et al., J. Sound and Vibration, 333, No. 4, 1097–1118 (2014). https://doi.org/10.1016/j.jsv.2013.09.033

    Article  ADS  Google Scholar 

  26. S.A.Ambarzumyan and A.A. Khachatryan, Mekhan. Tverd. Tela, 2, 44–53 (1966).

    Google Scholar 

  27. R. M. Jones, AIAA J., 15, No. 1, 16–23 (1977). https://doi.org/10.2514/3.7297

    Article  ADS  Google Scholar 

  28. O. A.Vasil’eva and O.V.Rudenko, Acoust. Phys., 66, No. 3, 235–241 (2020). https://doi.org/10.1134/S1063771020030070

  29. N.N.Nefedov and O.V.Rudenko, Dokl. Math., 102, No. 1, 283–287 (2020). https://doi.org/10.1134/S1064562420040146

    Article  MathSciNet  Google Scholar 

  30. V. A.Gusev and D. A. Zharkov, Bull Rus. Acad. Sci. Phys., 87, No. 4, 524–527 (2023). https://doi.org/10.3103/S1062873822701593

    Article  Google Scholar 

  31. O.V.Rudenko and C. M.Hedberg, Acoust. Phys., 64, No. 4, 422-431 (2018). https://doi.org/10.1134/S1063771018040127

    Article  ADS  Google Scholar 

  32. V.E. Nazarov, S. B.Kiyashko, and A. V. Radostin, Radiophys. Quantum Electron., 61, No. 6, 418–425 (2018). https://doi.org/10.1007/s11141-018-9903-6

    Article  ADS  Google Scholar 

  33. V.E. Nazarov and S. B.Kiyashko, Radiophys. Quantum Electron., 61, No. 6, 426–435 (2018). https://doi.org/10.1007/s11141-018-9904-5

    Article  ADS  Google Scholar 

  34. V.E. Nazarov and S. B.Kiyashko, Russian J. Nonlinear Dyn., 14, No. 3, 331–342 (2018). https://doi.org/10.20537/nd180304

  35. V.E. Nazarov and S. B.Kiyashko, Wave Motion, 106, 102772 (2021). https://doi.org/10.1016/j.wavemoti.2021.102772

    Article  Google Scholar 

  36. V.E. Nazarov, A. B.Kolpakov, and A. V. Radostin, Acoust. Phys., 56, No. 5, 632–636 (2010). https://doi.org/10.1134/S1063771010050052

    Article  ADS  Google Scholar 

  37. J. M. Cormack, T. G. Muir, and M. F. Hamilton, Proc. Meetings on Acoustics, 36, 045003 (2019). https://doi.org/10.1121/2.0001065

  38. V.E. Nazarov, Phys. Met. Metallogr ., 88, No. 4, 390–398 (1999).

    Google Scholar 

  39. V.E. Nazarov, Acoust. Phys., 46, No. 2, 186–190 (2000).

    Article  ADS  Google Scholar 

  40. V.E. Nazarov, A. V. Radostin, and I. A. Soustova, Acoust. Phys., 48, No. 1, 76–80 (2002). https://doi.org/10.1134/1.1435393

    Article  ADS  Google Scholar 

  41. V.E. Nazarov and A. V. Radostin, Acoust. Phys., 50, No. 4, 446–453 (2004). https://doi.org/10.1134/1.1776223

    Article  ADS  Google Scholar 

  42. P. A. Elmore and M.A.Breazeale, Ultrasonics, 41, No. 9, 709–718 (2004). https://doi.org/10.1016/j.ultras.2003.11.001

    Article  Google Scholar 

  43. J. K. Na and M.A.Breazeale, JASA, 95, No. 6, 3213–3221 (1994). https://doi.org/10.1121/1.409985

    Article  Google Scholar 

  44. V.E. Nazarov and L. A.Ostrovskiy, Sov. Phys. Acoust., 36, No. 1, 57–60 (1990).

    Google Scholar 

  45. V.E. Nazarov, S. B.Kiyashko, and A. V. Radostin, Radiophys. Quantum Electron., 58, No. 10, 729–737 (2016). https://doi.org/10.1007/s11141-016-9645-2

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. A. V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia

    V. E. Nazarov & S. B. Kiyashko

Authors
  1. V. E. Nazarov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. B. Kiyashko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. E. Nazarov.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 66, No. 4, pp. 276–288, April 2023. Russian DOI: https://doi.org/10.52452/00213462_2023_66_04_276

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nazarov, V.E., Kiyashko, S.B. Longitudinal Waves in Structurally Inhomogeneous Viscoelastic Solids with a Quadratic–Bimodular Nonlinearity Decreasing with Increasing Frequency. Radiophys Quantum El 66, 248–259 (2023). https://doi.org/10.1007/s11141-024-10291-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11141-024-10291-1

Search

Navigation