Fundamental and generalized solutions of the equations of the non-stationary dynamics of thermoelastic rods

Abstract

The equations of unbound thermoelasticity in the spatially one-dimensional case are considered that describe the
dynamics of rods with allowance for their thermoelastic properties for longitudinal vibrations. A generalized Fourier transform of
the matrix of fundamental solutions is constructed and its regularization is carried out to reconstruct the original of the Green’s
tensor. The Green’s tensor of the equations of unbound thermoelasticity is constructed, which describes the thermodynamics
of the medium under the action of instant concentrated power and thermal sources. Generalized solutions of the equations of
unbound thermoelasticity are obtained and their regular integral representations are given.