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Rheological Models and the Equations of State of the Micro- and Structurally Inhomogeneous Media with Frequency-Dependent Nonlinearity

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We propose rheological models of micro- and structurally inhomogeneous media, which explain an increase in their acoustic nonlinearity with increasing wave frequency. The equations of state for such media are obtained and the frequency dependences of the nonlinearity parameters for the processes of generation of the second harmonic and the difference frequency are determined for the media with quadratic elastic nonlinearity.

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References

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

  2. L. K. Zarembo and V. A. Krasil’nikov, Sov. Phys. Usp., 13, No. 6, 778–797 (1971). https://doi.org/10.1070/PU1971v013n06ABEH004281.

    Article  ADS  Google Scholar 

  3. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Butterworth-Heinemann, Oxford (1986).

    MATH  Google Scholar 

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

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

    Google Scholar 

  6. 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 

  7. V. E. Nazarov and A. V. Radostin, Nonlinear Acoustic Waves in Micro-Inhomogeneous Solids, Wiley, Chichester (2015).

    Google Scholar 

  8. L. A. Ostrovskii, Sov. Phys. Acoust., 34, No. 5, 523 (1988).

    Google Scholar 

  9. L. A. Ostrovskii, Sov. Phys. Acoust., 35, No. 3, 286 (1989).

    Google Scholar 

  10. L. A. Ostrovskii and P. A. Johnson, Rivista Nuovo Cim., 24, Ser. 4, No. 7, 1 (2001).

  11. V. E. Nazarov, L. A. Ostrovskii, I. A. Soustova, and A. M. Sutin, Sov. Phys. Acoust., 34, No. 3, 285 (1988).

    Google Scholar 

  12. 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 

  13. V. E. Nazarov, A. V. Radostin, L. A. Ostrovsky, and I. A. Soustova, Acoust. Phys., 49, No. 4, 444–448 (2003). https://doi.org/10.1134/1.1591300.

    Article  ADS  Google Scholar 

  14. V. E. Nazarov and L. A. Ostrovskii, Sov. Phys. Acoust., 36, No. 1, 57 (1990).

    Google Scholar 

  15. W.P. Mason, ed., Physical Acoustics, V. 3, Pt. B, Principles and Methods, Lattice Dynamics, Academic Press, New York (1965).

  16. S. Ya. Kogan, Fiz. Zemli, No. 11, 3–28 (1966).

    Google Scholar 

  17. V. E. Nazarov, V. Yu. Zaitsev, and I. Yu. Belyaeva, Acoust. Lett., 22, No. 12, 236–241 (1999).

    Google Scholar 

  18. V. Yu. Zaitsev, V. E. Nazarov, and I. Yu. Belyaeva, Acoust. Phys., 47, No. 2, 178–183 (2001). https://doi.org/10.1134/1.1355802.

    Article  ADS  Google Scholar 

  19. V. E. Nazarov, V. Yu. Zaitsev, and I. Yu. Beliaeva, Acta Acust. united Ac., 88, No. 1, 40–49 (2002).

    Google Scholar 

  20. L. A. Ostrovskii, Radiophys. Quantum Electron., 19, No. 5, 464–486 (1976). https://doi.org/10.1007/BF01034467.

    Article  ADS  Google Scholar 

  21. L. A. Ostrovsky and A. I. Potapov, Introduction to the Theory of Modulated Waves [in Russian], Fizmatlit, Moscow (2003).

    Google Scholar 

  22. D. V. Sivukhin, General Course of Physics, Vol. 5, Atomic and Nuclear Physics [in Russian], Fizmatlit, Moscow (2002).

  23. V. E. Nazarov and A. V. Radostin, Acoust. Phys., 51, No. 2, 230–235 (2005). https://doi.org/10.1134/1.1884498.

    Article  ADS  Google Scholar 

  24. V. E. Nazarov, Wave Motion, 51, No. 1, 10–22 (2014). https://doi.org/10.1016/j.wavemoti.2013.04.006.

    Article  Google Scholar 

  25. V. E. Nazarov, S. B. Kiyashko, and A. V. Radostin, Radiophys. Quantum Electron., 59, No. 3, 246–256 (2016). https://doi.org/10.1007/s11141-016-9693-7.

    Article  ADS  Google Scholar 

  26. J. K. Na and M. A. Breazeale, J. Acoust. Soc. Am., 95, No. 3, 3213–3221 (1995). https://doi.org/10.1121/1.409985.

    Article  ADS  Google Scholar 

  27. P. A. Elmore and M. A. Breazeale, Ultrasonics, 41, 709–718 (2004). https://doi.org/10.1016/j.ultras.2003.11.001.

    Article  Google Scholar 

  28. R. M. Davis, Stress Waves in Solids, Cambridge Univ. Press, Cambridge (1956).

    Google Scholar 

  29. O. V. Rudenko and S. I. Soluyan, Theoretical Foundations of Nonlinear Acoustics, Consultants Bureau, New York (1977).

    Book  Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia

    V. E. Nazarov & S. B. Kiyashko

Authors
  1. V. E. Nazarov
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  2. S. B. Kiyashko
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Correspondence to V. E. Nazarov.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 63, No. 1, pp. 70–78, January 2020.

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Nazarov, V.E., Kiyashko, S.B. Rheological Models and the Equations of State of the Micro- and Structurally Inhomogeneous Media with Frequency-Dependent Nonlinearity. Radiophys Quantum El 63, 64–72 (2020). https://doi.org/10.1007/s11141-020-10035-x

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  • DOI: https://doi.org/10.1007/s11141-020-10035-x

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