Abstract
Abstract Elastic rod elements the axial line of which in the natural state is a planar curve that remains plane after loading are considered. The following assumptions are used: transverse normal cross sections, planar before deformation, preserve their plane shape and normal orientation to the deformed thermoelastic axial line after deformation; the temperature field is stationary and nonuniform. The nonlinear equations of rod motion are derived with account for the rotational inertia of the cross section and the extensibility of the axial line. As a special case, the equations of small free oscillations of straight rods are written out and the natural frequencies are determined. The effect of the temperature gradient on the first natural frequency is investigated. The numerical calculations are carried out in the mathematical software Mathcad.