Dynamics of Viscoelastic Media with Internal Oscillators

Abstract

The viscoelastic constitutive laws for stresses and strains with time derivatives of high orders are considered. The concept of masses of internal oscillators is introduced for the interpretation of Theological coefficients. The weak nonlinear processes are studied using small parameter expansions. The transition to a moving coordinate system with the introduction of fast time and fast space coordinates gives the evolution equation, which is a generalization of the Burgers-Korteweg-de Vries case because of the inclusion of higher space derivatives. The suggested mathematical model corresponds to bounded intervals of dominant frequencies. The applications are connected with the analysis of waves in real geological media with fragmental microstructure.