Using the perturbation method, we study the processes of nonlinear propagation of the initially harmonic elastic waves in micro-inhomogeneous media, namely, polycrystalline solids with hysteresis-loss saturation and relaxation. The media with the basic hysteresis types, elastic and inelastic, are considered. The efficient nonlinearity parameters of such media are determined for the processes of self-action of a quasiharmonic wave and generation of its higher harmonics.
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References
L. K. Zarembo and V. A. Krasil’nikov, Introduction to Nonlinear Acoustics [in Russian], Nauka, Moscow (1966).
O. V. Rudenko and S. I. Soluyan, Theoretical Foundations of Nonlinear Acoustics, Consultants Bureau, New York (1977).
L. K. Zarembo and V. A. Krasil’nikov, Sov. Phys. Uspekhi, 13, No. 6, 778 (1971).
L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Butterworth–Heinemann, Oxford (1987).
L. D. Landau and E. M. Lifshitz, Theory of Elasticity Butterworth-Heinemann, Oxford (1986).
K. A. Naugol’nykh and L. A. Ostrovsky, Nonlinear Wave Processes in Acoustics, Cambridge Univ. Press, Cambridge (1998).
M. F. Hamilton and D. T. Blackstock, Nonlinear Acoustics, Academic Press, New York (1988).
M. A. Isakovich, General Acoustics [in Russian], Nauka, Moscow (1973).
S. N. Gurbatov, O. V. Rudenko, and A. I. Saichev, Waves and Structures in Nonlinear Nondispersive Media, Springer, Berlin (2011).
V. E. Nazarov, L. A. Ostrovsky, I. A. Soustova, and A. M. Sutin, Phys. Earth Planet. Inter., 50, No. 1, 65 (1988).
L. A. Ostrovsky and P. A. Johnson, Riv. Nuovo Cim., 24, Ser. 4, No. 7, 1 (2001).
O. V. Rudenko, Physics—Uspekhi ,49, No. 1, 69 (2006).
R. A. Guyer and P. A. Johnson, Nonlinear Mesoscopic Elasticity: The Complex Behavior of Granular Media Including Rocks and Soil, Wiley-VCH, Weinheim (2009).
V. E. Nazarov, Fiz. Met. Metalloved., 88, No. 4, 82 (1999).
V. E. Nazarov, Acoust. Phys., 46, No. 2, 186 (2000).
V. E. Nazarov, A. V. Radostin, and I. A. Soustova, Acoust. Phys., 48, No. 1, 76 (2002).
V. E. Nazarov and A. V. Radostin, Acoust. Phys., 50, No. 4, 446 (2004).
V. E. Nazarov, A. B. Kolpakov, and A. V. Radostin, Fiz. Mezomekh., 13, No. 2, 41 (2010).
V. E. Nazarov and A. V. Radostin, Nonlinear Acoustic Waves in Micro-Inhomogeneous Solids, Wiley, Hoboken (2015).
N. N. Davidenkov, Zh. Tekh. Fiz., 8, No. 6, 483 (1938).
A. V. Granato and K. J. Lücke, J. Appl. Phys., 27, No. 6, 583 (1956).
S. Asano, J. Phys. Soc. Jpn., 29, No. 4, 952 (1970).
A. B. Lebedev, Phys. Solid State, 41, No. 7, 1105 (1999).
V. E. Nazarov and A. V. Radostin, Fiz. Zemli, 413, No. 2, 85 (2003).
V. E. Nazarov and A. M. Sutin, Sov. Phys. Acoust., 35, No. 4, 410 (1989).
V. E. Nazarov, A. V. Radostin, L. A. Ostrovsky, and I. A. Soustova, Acoust. Phys., 49, No. 3, 344 (2003).
V. E. Nazarov, V. Yu. Zaitsev, and I. Yu. Beliaeva, Acoust. Lett., 22, No. 12, 236 (1999).
V. E. Nazarov, V. Yu. Zaitsev, and I. Yu. Beliaeva, Acta Acust. United Ac., 88, No. 1, 40 (2002).
D. Niblett and J. Wilks, Usp. Fiz. Nauk, 80, No. 1, 125 (1963).
V. E. Nazarov, Sov. Phys. Acoust., 37, No. 1, 75 (1991).
V. E. Nazarov and A. B. Kolpakov, J. Acoust. Soc. Am., 107, No. 4, 1915 (2000).
S. N. Golyandin, K. V. Sapozhnikov, Yu. A. Emel’yanov, et al., Phys. Solid State, 40, No. 10, 1667 (1998).
S. N. Golyandin, K. V. Sapozhnikov, and S. B. Kustov, Phys. Solid State, 47, No. 4, 638 (2005).
K. V. Sapozhnikov, S. N. Golyandin, and S. B. Kustov, Phys. Solid State, 52, No. 1, 43 (2010).
K. V. Sapozhnikov, S. N. Golyandin, and S. B. Kustov, Phys. Solid State, 52, No. 12, 2501 (2010).
D. V. Sivukhin, General Course of Physics, Electricity [in Russian], Fizmatlit, Moscow (2004).
V. E. Nazarov and S. B. Kiyashko, Radiophys. Quantum Electron., 56, No. 10, 686 (2013).
V. E. Nazarov and S. B. Kiyashko, Radiophys. Quantum Electron., 59, No. 2, 111 (2016).
V. E. Nazarov, A. V. Radostin, L. A. Ostrovsky, and I. A. Soustova, Acoust. Phys., 49, No. 4, 444 (2003).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 62, No. 5, pp. 390–402, May 2019.
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Nazarov, V.E., Kiyashko, S.B. Nonlinear Wave Processes in Polycristalline Solids with Hysteresis-Loss Saturation and Relaxation. Radiophys Quantum El 62, 348–360 (2019). https://doi.org/10.1007/s11141-019-09982-x
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DOI: https://doi.org/10.1007/s11141-019-09982-x