THE METHOD OF AVERAGING IN DYNAMIC PROBLEMS OF THE THEORY OF THE ELASTICITY OF STRUCTURALLY INHOMOGENEOUS-MEDIA

A modification of the method of averaging to construct approximate solutions of the dynamic equations of the theory of the elasticity of an inhomogeneous medium as the synthesis of successive approximation with a probabilistic approach is considered. To find the zero-th approximation we assume the material coefficients of the medium to be random functions of the spatial coordinates, one form of which is the elastic moduli and the density of this specific medium. In the zero-th approximation the inhomogeneous medium under consideration is described by an effective medium possessing spatial dispersion. The first approximation takes account of the influence of structural singularities of this specific realization on the displacement field configuration of the propagating waves. Error estimates are given for the zero-th approximation. The dynamics of inhomogenous media is described by equations with variable coefficients whose approximate methods of solution have been developed intensively. Different modifications of the averaging method were examined for example, in /1-5/. The method of using the averaging method for discretely laminar structures is described in /1/. An analogous scheme is developed in this paper for the dynamic equations of the theory of the elasticity of inhomogeneous media.