Nonlinear Elastic Waves in Crystalline Solids with Granato–Lucke Dislocation Hysteresis

We perform theoretical and numerical studies of nonlinear propagation and distortion of elastic initially harmonic waves in crystalline solids with Granato–Lucke dislocation hysteresis. We obtain analytical solutions describing nonlinear propagation and evolution of waves in such media. The amplitude dependences of the nonlinear decay decrements and changes in the propagation velocity of the fundamental-frequency wave, as well as the amplitudes of its higher harmonics are determined. A graphical analysis of the solutions obtained is carried out.