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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

  • I. V. Kudinov
  • V. A. Kudinov
HEAT CONDUCTION AND HEAT EXCHANGE IN TECHNOLOGICAL PROCESSES

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 infinite 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.

Keywords

dynamic thermoelasticity hyperbolic heat-conduction equation stress jump undamped thermoelastic stress waves relaxation coefficient 

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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Samara State Technical UniversitySamaraRussia

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