Modified Davidenkov hysteresis and the propagation of sawtooth waves in polycrystals with hysteresis loss saturation

Abstract

A modified Davidenkov hysteresis equation of the state has been proposed for describing the saturation of the effects of amplitude-dependent internal friction in polycrystalline metals and other solids, which possess imperfect elasticity. Using this equation, an exact analytical solution of the problem of the propagation of a periodic sawtooth wave in media characterized by quadratic hysteresis with nonlinear loss saturation has been obtained. Regularities of variations in the characteristics of a sawtooth wave, such as nonlinear loss, the change in the velocity of the propagation of the wave, and the amplitudes of the higher harmonics of the wave, have been determined. A graphical analysis of the evolution of the shape and the spectral components of the wave has been carried out.