Nonlinear Effects in Crystalline Solids with Saturation of Amplitude-Dependent Internal Friction Decreasing with Frequency Growth

As a result of the modification of quasi-static elastic and nonelastic hysteresis, dynamic hysteresis equations of state of crystalline solids with frequency-dependent saturation of the amplitude-dependent internal friction that decreases with increasing frequency, have been proposed. The perturbation method has been used to study the nonlinear propagation of initially harmonic longitudinal elastic waves in rods made of such materials. Numerical, graphical, and comparative analysis of the obtained solutions has been performed and the typical amplitude-frequency dependences of nonlinear wave effects have been revealed. A technique has been proposed for determining the type of dynamic hysteresis for crystalline solids with frequency-dependent saturation of the amplitude-dependent internal friction.