DETERMINATION OF THE DYNAMIC STRESSES IN AN INFINITE PLATE ON THE BASIS OF AN EXACT ANALYTICAL SOLUTION OF THE HYPERBOLIC HEAT-CONDUCTION EQUATION FOR IT

With the use of an exact analytical solution of the classical hyperbolic heat-conduction equation, derived on the basis of the Maxwell–Cattaneo–Luikov relaxation formula, an exact analytical solution of the problem on the dynamic thermoelasticity of an infi nite plate was obtained for the case where the outer surfaces of this plate are free of mechanical loads. It is shown that the undamped thermoelastic stresses in this plate vary spasmodically in time with periodic change in their sign. The stress jumps arising near the opposite outer surfaces of the indicated plate move along the spatial variable to its center where they superimpose, with the result that the dynamic thermal stresses in the plate double.
   
Author:  I. V. Kudinov and V. A. Kudinov
Keywords:  dynamic thermoelasticity, hyperbolic heat-conduction equation, stress jump, undamped thermoelastic stress waves, relaxation coefficient
Page:  398