Proceedings of the International scientific and practical conference ―Science at the Frontier of Civilizations: Challenges and Perspectives‖ (December 27-29, 2025) / Publisher website: www.naukainfo.com. – Helsinki, Finland, 2026. – 252 p.

189 obtained for the case where the slot temperatures vary according to a linear law and overheating occurs in one of the slots, for example due to blockage. The solution for the case of overheating in several slots is obtained using the superposition principle, owing to the linearity of the problem. When determining rotor deflections, the rotor is considered as a beam with a piecewise constant cross section, hinged at both ends. For this purpose, fourth-order differential equations of thermal bending are used. This approach eliminates the need for additional considerations that sometimes arise when using second-order thermal bending equations. At the boundaries of the rotor barrel, continuity conditions are satisfied for deflections, rotation angles, bending moments, and shear forces, while standard hinged boundary conditions are applied at the rotor ends. Based on the obtained solutions, the dependence of rotor deflection on the orientation of the overheated slot, the number of overheated slots, and the ratio of the thermal conductivity of the intermediate layer materials to that of the rotor material is investigated. The results show that an increase in the thermal conductivity of the intermediate layer leads to an increase in the temperature analog of the bending moment and the resulting maximum rotor deflection, as well as a corresponding increase in vibration levels. Thus, by solving the problem of forced vibrations of a rotor with a known initial deflection, it is possible to determine the vibration level of the rotor under asymmetric temperature field conditions. It should be noted that the accuracy of the obtained results can be significantly affected by the reliability of the initial data related to the dynamic characteristics of the supports, damping, and other factors. It is known that the thermal deflection of a rotor corresponds to a certain mechanical imbalance and can be compensated by installing appropriately symmetric or skew- symmetric balancing weights.