Approximate Solution of a Three-Dimensional Problem of Elastic Diffusion in an Orthotropic Layer

Abstract

We consider a three-dimensional nonstationary problem for an elastic layer with regard for diffusion and use a model of mechanical diffusion under the conditions of local equilibrium. The model includes a coupled system of equations of motion of the elastic body and the mass transfer equation. The asymptotic procedure of separation of variables is applied. This procedure enables us to reduce the multidimensional problem to a recursion sequence of one-dimensional problems solved with the help of Fourier series and the Laplace transformation with respect to time. The originals of the transforms of unknown functions are determined analytically.