Amplitude-Dependent Internal Friction and Harmonic Generation in Media with Hysteresis Nonlinearity and Linear Dissipation

Abstract

Based on generalization and integration of models for dislocation mechanisms of the hysteresis nonlinearity, we propose a hysteresis equation of state of polycrystalline solids with saturated amplitude-dependent losses. Using the perturbation method, we study, both theoretically and numerically, the nonlinear effects during propagation of acoustic waves in the media with hysteresis nonlinearity and linear viscous dissipation. Nonlinear damping rate and propagation velocity of the wave at the fundamental frequency, as well as regularities for the amplitudes and phase velocities at its second and third harmonics, are determined. It is shown that the media described by such hysteresis equations of state have a nonlinear dispersion, which leads to a nonmonotonic rise and amplitude beats of the higher harmonics as the wave amplitude increases at the fundamental frequency.