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A physical model of stress-strain dynamics and long-time relaxation (slow time) in structured media is proposed. The model is based on the analysis of inter-grain contacts and the resulting surface force potential with a barrier. The result is a unified description of the classical acoustic nonlinearity, stress-strain hysteresis, and logarithmic relaxation law for sound velocity (and, hence, for the frequency of nonlinear resonance in samples of structured materials). Estimates of a characteristic volume of interacting contacts give close values for the variety of consolidated materials. For weak (linear) testing waves, the logarithmic relaxation occurs if a classical quadratic nonlinearity is added to the stress-strain relation. [ABSTRACT FROM AUTHOR]

The material of the correlated report delivered at the 18th International Symposium on Nonlinear Acoustics (ISNA-18) in July 2008 (Stockholm, Sweden) [1] is presented in a more comprehensive form [1]. These results have also been partially reported on in the lectures given at the 12th and 13th “Nonlinear Waves“ schools in Nizhni Novgorod [2, 3]. The aim of the paper is to briefly consider the directions of the development of nonlinear acoustics and its successes which have been at the center of attention lately. [ABSTRACT FROM AUTHOR]

Nonlinear processes caused by the propagation of low-frequency and high-frequency acoustic pulses in an unbounded medium and the propagation of continuous waves in a ring resonator are theoretically studied on the basis of two hysteretic equations of state for media with imperfect elasticity. The profiles and parameters of pulses, the resonance curve and the Q factor of the resonator, and the ratio of the nonlinear resonance frequency shift to the nonlinear damping decrement are determined. For nonlinear wave processes in such media, the distinctive features that allow one to choose an appropriate hysteretic equation of state for analytically describing the experimental data are revealed. © 2003 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]