Nonlinear acoustic waves in media with hysteresis and long-time relaxation

Abstract

It is known that the media with complex structures (e.g., rocks and ceramics) possess an anomalously strong elastic nonlinearity. Nonlinear acoustic effects are used in a number of important applications, such as seismic waves (earthquakes), non-destructive testing, and contact physics. Two specific features were registered, in most of the experiments: hysteresis in the stress-strain relation and longtime relaxation (slow time). Some physical models, mostly phenomenological, have been suggested to explain these phenomena. However, there are very few works considering the effect of medium hysteresis and relaxation on wave propagation and oscillations in resonators. This presentation is a review of both published and new results in this area. Among the problems discussed are: (1) A brief overview of experiments and models; (2) Analysis of wave propagation in simplified models of media with hysteresis as opposed to the nonlinear waves in media characterized by elastic constants of second and third order; (3) Theory of wave interaction in resonators with hysteresis; (4) Study of waves in media with slow time relaxation; (5) Some data from laboratory and field experiments; (6) Some unsolved issues and the relevant future work will be outlined in conclusion.