Generalized solutions of boundary value problems of dynamics thermoelastic rods

Abstract

The non-stationary boundary-value problems of the dynamics of thermoelastic rods are considered. Based on the method of generalized functions, generalized solutions of boundary value problems are constructed using a model of unbound thermoelasticity under the influence of non-stationary power and thermal loads of various types. The integral representations of the solution of the boundary-value problem are given, which make it possible to determine the thermally stressed state of the rod under the influence of various power and thermal influences from the known boundary displacements, stresses, temperature, and heat fluxes at the ends of the rod.