The Solution of Cauchy Problem of Thermoelastic Rod Dynamicsby Generalized Functions Method

This is the authors' abstract. We don't add key points for this paper.

The Cauchy problem is considered about the dynamics of a thermoelastic rod by the action of different force and heat effects under arbitrary initial conditions. Using the Green's tensor of the thermoelasticity equations, an analytical solution to the problem was obtained, allowing one to determine the deformations, stresses, and temperature in any cross-section of the rod and at any time, if its initial state and the acting force and heat sources are known. Numerical calculations of temperature and displacements under the action of pulsed concentrated force and heat sources are given. Calculations of the solution of the Cauchy problem under the action of regular force and heat sources distributed along the rod are performed. The developed program allows one to study thermodynamic processes in rods with various physical and mechanical parameters under the action of distributed, concentrated, and pulsed heat and force sources, described by singular generalized functions.