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    Veniamin Nazarov

    Ul’yanova str. 46, Nighniy Novgorod, 603950, Russia
    Institute of Applied Physics, Russian Academy of Sciences


    Nazarov V. E., Kiyashko S. B.
    On the basis of experimental data of the study of amplitude-dependent internal friction phenomena in polycrystalline solids the inelastic hysteretic state equation with a saturation of nonlinear losses is proposed. Theoretical analysis of the asymmetric saw-tooth waves propagation in such media is carried out. The regularities (amplitude dependent losses and changes in the propagation velocity) are determined for the characteristics of nonlinear wave and its higher harmonic amplitudes. The graphical analysis of form of the wave and evolution of its spectral components is carried out.
    Keywords: hysteresis, amplitude-dependent internal friction, saturation of nonlinear losses, sawtooth acoustic waves
    Citation: Nazarov V. E., Kiyashko S. B.,  Saw-tooth waves in hysteretic media with a saturation of nonlinear losses, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 4, pp.  647–655
    Nazarov V. E., Kiyashko S. B., Radostin A. V.
    The results of research of the propagation of longitudinal acoustic waves in media with bimodular elastic nonlinearity and relaxation are presented. Analytical exact solutions have been obtained for the profiles of asymmetrical stationary waves as well as self-similar pulses and periodical waves propagating without distortions in their form.
    Keywords: bimodular nonlinearity, relaxation, nonlinear waves, self-similar solutions
    Citation: Nazarov V. E., Kiyashko S. B., Radostin A. V.,  Self-similar waves in media with bimodular elastic nonlinearity and relaxation, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 2, pp.  209-218
    Nazarov V. E., Kiyashko S. B.
    Theoretical and numerical study of nonlinear wave processes in media with hysteretic nonlinearity are carried out. The phenomena of amplitude-dependent damping as well as change of the propagation velocity of harmonic wave and its second and third harmonic generation are considered. It was shown that the hysteretic media possess nonlinear dispersion that become apparent in the difference between the phase velocities of strong harmonic pump wave and its weak high harmonics. The dispersion leads to both spatial beatings and non-monotonically rate of growth of an amplitude of high harmonic at the increase in amplitude of basic frequency wave.
    Keywords: hysteresis, amplitude-dependent internal friction, harmonics generation, nonlinear dispersion
    Citation: Nazarov V. E., Kiyashko S. B.,  Amplitude-dependent internal friction and harmonics generation in solids with histeretic nonlinearity, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 3, pp.  297-307

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