Mathematical modeling of dynamic interaction of a rod with a deformable medium

In this article, the developed approach is used to derive the equations of oscillations of round rods, taking into account the viscosity of the rod material, the influence of the environment and temperature. The exact and approximate equations of torsional and longitudinal vibrations of a round rod are obtained. When describing a rod in a deformable medium, three contact conditions are considered: the absence of friction (smooth contact), the friction between the rod and the medium according to Coulomb's law, and the hard contact.