Borshch O. Bending wave and vibration processes in rotating rods prestressed by longitudinal forces and torques with internal flows of liquid

The dissertation is devoted to the statement and solution of new problems about vibrations of long rotating tubes under action of different nature loads. The analysis of precision of beam theories based on the Bernoulli-Euler and S.P. Timoshenko hypotheses is performed, the more precise mathematical models of beam dynamics, founded on taking into consideration of momentum moments of their elements (spin effects) are proposed. The wave equations of tube rods are deduced with attention to the Coriolis inertia forces, longitudinal forces and torques. With the use of dispersion methods, the general regularities of the dynamic processes realization are established for the loads of considered types. It is shown that natural vibrations can be realized only in the mode of spiral waves. The problem about investigation of whirling vibration of the bottom part of a drill column under action of the cutting moment is considered. The computer simulation of the process of the vibration auto-excitation is fulfilled.