Dynamic characteristics of nonlinear interaction in elastic medium

Abstract

Traditionally, an acoustic wave process is analyzed in terms of sound pressure and/or sound velocity. The dynamic distortion of the wave profile, however, is complicated by contribution of both quadratic and cubic nonlinearities of the elastic medium. This condition necessitates expanding a range of variables to include particle and wave accelerations. As dynamic characteristics, particle and wave accelerations fully complement analysis of dynamic and inert properties of the elastic medium. The Riemanns solution, in which the quadratic and cubic nonlinearities are accounted for through respective derivatives of the sound velocity, allows for a new and different perspective on the aforementioned properties. For a simple wave with contribution of the quadratic nonlinearity only, the acceleration profile describing dynamics of wave deformation varies symmetrically relative to the discontinuity region. The cubic nonlinearity leads to more complex acceleration profile with asymmetric properties, which can be discerned and assessed using a combination of numerical and graphical methods. Such an approach is quite effective and vivid in separating contributions of quadratic and cubic nonlinearities. An integral nonlinear parameter N, introduced on the basis of this analysis, is proposed for estimating ability of the fluidlike medium to support effective propagation and nonlinear interaction of acoustic waves.