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Radiophysics and Quantum Electronics

, Volume 61, Issue 6, pp 426–435 | Cite as

Interaction of Acoustic Waves in The Media with Quadratically Bimodular Nonlinearity

  • V. E. Nazarov
  • S. B. Kiyashko
Article
  • 9 Downloads

We obtain the quadratically bimodular equation of state for a rod with cracks on the basis of a model of the crack as an elastic contact of rough surfaces of solids. The perturbation method is used to theoretically study the propagation and interaction of collinear longitudinal elastic (strong low-frequency and weak high-frequency) waves in such media. Expressions for the amplitudes of the secondary waves, namely, the second and the fourth harmonics of the strong wave, the second harmonic of the weak wave, and the combination-frequency waves are obtained.

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References

  1. 1.
    L.K. Zarembo and V. A. Krasil’nikov, Introduction to Nonlinear Acoustics [in Russian], Nauka, Moscow (1966).Google Scholar
  2. 2.
    L. K. Zarembo and V. A. Krasil’nikov, Sov. Phys. Uspekhi, 13, No. 6, 778 (1971).ADSCrossRefGoogle Scholar
  3. 3.
    O.V. Rudenko and S. I. Soluyan, Theoretical Foundation of Nonlinear Acoustics, Springer, New York (1977).CrossRefGoogle Scholar
  4. 4.
    K. A. Naugol’nykh and L. A. Ostrovsky, Nonlinear Wave Processes in Acoustics, Cambridge University Press, Cambridge (1998).Google Scholar
  5. 5.
    L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Butterworth-Heinemann, Oxford (1986).zbMATHGoogle Scholar
  6. 6.
    G. V. Egorov and É. I. Mashinsky, Tekhnol. Seismoraz., No. 1, 72 (2011).Google Scholar
  7. 7.
    M. A. Isakovich, General Acoustics [in Russian], Nauka, Moscow (1978).Google Scholar
  8. 8.
    S. A. Ambartsumyan, Bimodular Theory of Elasticity [in Russian], Nauka, Moscow (1982).Google Scholar
  9. 9.
    V. E. Nazarov, S. B. Kiyashko, and A. V. Radostin, Radiophys. Quantum Electron., 61, No. 6, 418 (2018).CrossRefGoogle Scholar
  10. 10.
    V. E. Nazarov and A. M. Sutin, J. Acoust. Soc. Am., 102, No. 6, 3349 (1997).ADSCrossRefGoogle Scholar
  11. 11.
    B. B. Mandelbrot, D. E. Passoja, and A. J. Paulay, Nature, 308, 721 (1984).ADSCrossRefGoogle Scholar
  12. 12.
    B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco (1982).zbMATHGoogle Scholar
  13. 13.
    J. A. Greenwood and J. B. P. Williamson, Proc. Roy. Soc. A, 295, 300 (1996).ADSCrossRefGoogle Scholar
  14. 14.
    K. L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge (1985).CrossRefGoogle Scholar
  15. 15.
    I. Sneddon, Fourier Transformations, Courier Corporation, New York (1951).Google Scholar
  16. 16.
    M. Kachanov, Adv. Appl. Mech., 30, 259 (1994).CrossRefGoogle Scholar
  17. 17.
    V. Yu. Zaitsev and P. Sas, Acta Acust. United Ac., 86, 216 (2000).Google Scholar
  18. 18.
    V. Aleshin and K. van den Abeele, J. Mech. Phys. Solids, 55, 765 (2007).ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, McGraw-Hill, New York (1970).zbMATHGoogle Scholar
  20. 20.
    J. Mathews and R. L. Walker, Mathematical Methods of Physics, W.A. Benjamin, New York (1964).zbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Applied Physics of the Russian Academy of SciencesNizhny NovgorodRussia

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