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An Intense Wave in Defective Media Containing Both Quadratic and Modular Nonlinearities: Shock Waves, Harmonics, and Nondestructive Testing

  • Nonlinear Acoustics
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Abstract

The observed nonclassical power-law dependence of the amplitude of the second harmonic wave on the amplitude of a harmonic pump wave is explained as a phenomenon associated with two types of nonlinearity in a structurally inhomogeneous medium. An approach to solving the inverse problem of determining the nonlinearity parameters and the exponent in the above-mentioned dependence is demonstrated. To describe the effects of strongly pronounced nonlinearity, equations containing a double nonlinearity and generalizing the Hopf and Burgers equations are proposed. The possibility of their exact linearization is demonstrated. The profiles, spectral composition, and average wave intensity in such doubly nonlinear media are calculated. The shape of the shock front is found, and its width is estimated. The wave energy losses that depend on both nonlinearity parameters—quadratic and modular—are calculated.

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References

  1. A. I. Korobov and V. M. Prokhorov, Acoust. Phys. 62 (6), 681 (2016).

    Article  ADS  Google Scholar 

  2. A. I. Korobov, A. I. Kokshaiskii, V. M. Prokhorov, I. A. Evdokimov, S. A. Perfilov, and A. D. Volkov, Phys. Solid Stat. 58 (12), 2472 (2016).

    Article  ADS  Google Scholar 

  3. O. V. Rudenko, Dokl. Math. 94 (3), 703 (2016).

    Article  MathSciNet  Google Scholar 

  4. S. A. Ambartsumyan, Elasticity Theory of Different Moduli (China Rail. Publ. House, Beijing, 1986).

    Google Scholar 

  5. A. V. Radostin, V. E. Nazarov, and S. B. Kiyashko, Wave Motio. 50 (2), 191 (2013).

    Article  Google Scholar 

  6. V. E. Nazarov, S. B. Kiyashko, and A. V. Radostin, Radiophys. Quant. Electron. 58, 729 (2016).

    Article  ADS  Google Scholar 

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

    Google Scholar 

  8. S. N. Gurbatov, O. V. Rudenko, and A. I. Saichev, Waves and Structures in Nonlinear Nondispersive Media (Springer, Berlin, Heidelberg, 2011; Higher Education Press, Beijing, 2011).

    MATH  Google Scholar 

  9. O. V. Rudenko, Dokl. Math. 92 (2), 268 (2015).

    Google Scholar 

  10. O. V. Rudenko, Dokl. Math. 94 (3), 708 (2016).

    Article  Google Scholar 

  11. S. G. Mikhailov and O. V. Rudenko, Acoust. Phys. 63 (3), 270 (2017).

    Article  ADS  Google Scholar 

  12. O. V. Rudenko, Dokl. Math. 95 (3), 291 (2017).

    Article  MathSciNet  Google Scholar 

  13. O. V. Rudenko and C. M. Hedberg, Nonlinear Dyn. 89 (3), 1905 (2017).

    Article  Google Scholar 

  14. C. M. Hedberg and O. V. Rudenko, Nonlinear Dyn. 90 (3), 2083 (2017).

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Blekinge Institute of Technology, Karlskrona, 371 79, Sweden

    A. L. Gray & O. V. Rudenko

  2. Moscow State University, Moscow, 119991, Russia

    O. V. Rudenko

  3. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, 119991, Russia

    O. V. Rudenko

  4. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, 123242, Russia

    O. V. Rudenko

Authors
  1. A. L. Gray
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  2. O. V. Rudenko
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Correspondence to O. V. Rudenko.

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Original Russian Text © A.L. Gray, O.V. Rudenko, 2018, published in Akusticheskii Zhurnal, 2018, Vol. 64, No. 4, pp. 411–416.

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Gray, A.L., Rudenko, O.V. An Intense Wave in Defective Media Containing Both Quadratic and Modular Nonlinearities: Shock Waves, Harmonics, and Nondestructive Testing. Acoust. Phys. 64, 402–407 (2018). https://doi.org/10.1134/S1063771018040048

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  • DOI: https://doi.org/10.1134/S1063771018040048

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