(Igor Sikorsky Kyiv Polytechnic Institute, 2024) Kostyushko, I.; Shapovalov, H.
Abstract. Stability of non-conservatively loaded elastic and inelastic bodies - a classic section of deformable solid mechanics that has been of interest for many years. In this paper, we study the motion stability of a free rod subjected to a constant tracking force on one of its ends. The problem is interesting in practical application, as it can be viewed as a simplified model of a rocket moving under the action of a jet force. The defining ratio of the rod material is the Kelvin-Voigt model. The solution to the problem is presented as a decomposition of the beam function. The number of terms of this expansion is substantiated. The critical load values in the presence and absence of viscosity are determined. It is established that the existence of a non-zero value of the internal viscosity coefficient in the Kelvin-Voigt model leads to a significant reduction in the critical load value compared to the elastic rod model. The given analytical results are confirmed by numerical calculations.