On the basis of the equations of motion, Cauchy formulas, generalized Hooke's law, and compatibility conditions for the Saint-Venant strains, a system of determining equations of the dynamic problem of thermoelasticity in stresses is deduced for a homogeneous isotropic cylinder in an elliptic cylindrical coordinate system. This system is reduced to a system of consecutively correlated wave equations in which the equation for the first invariant of the stress tensor is independent. The initial conditions for the resolving functions are presented.
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