Unsteady one-dimensional thermoelastic cross-diffusion perturbations in a layer

Abstract

In the paper we present an algorithm for solving the unsteady problem of the thermoelastodiffusion perturbations propagation in a multicomponent layer. One-dimensional physicomechanical processes in the medium are described by the locally equilibrium model, including the equations of elastic medium motion, heat transfer and mass transfer with cross-diffusion effects. The unknown functions of displacement, temperature and concentration increments are sought in the integral form of convolution by time of the surface Green’s functions and boundary conditions. To find the Green’s functions, we use the integral Laplace transform with respect to time and the Fourier expansion into series by the spatial coordinate. It allows us to reduce the problem to system of linear algebraic equations. The originals of the Fourier series coefficients are found using known theorems and tables of operational calculus. Thus, the use of numerical algorithms is minimized and the surface Green’s functions are found. Calculation example is presented.