A new closed solution of the related dynamic problem of thermoelastic for a long cylinder in case of temperature change on its faces (boundary conditions of the 1st kind) has been built. The mathematical formulation of the problem in question includes linear equations of motion and thermal conductivity relative to the radial component of the displacement vector, as well as functions of temperature field change. To solve the problem, a mathematical apparatus is used to separate variables in the form of a generalized final integral transformation (instrument). The constructed design ratios make it possible to determine the stress-deformed state and temperature field of the elastic element under arbitrary temperature external influence. The influence of the rate of change of load and physical properties of the material on the inertial properties of the elastic system has been analyzed, as well as the parameters at which it is necessary to take into account the connectivity of mechanical and temperature fields have been determined.
Keywords: Long cylinder, associated thermoelastic problem, transient temperature impact, final integral transformations