The study of the Sommerfeld phenomenon in the eccentric overhung shaft-disk system considering internal and external depreciation and shear deformations

As a basic component of many rotary systems, the overhung shaft-disk system is exposed to the Sommerfeld phenomenon. Owing to the interaction between the electric driving source and the vibration system, this destructive phenomenon appears as a dynamic jump around the natural frequencies of the vibration system. This dynamic effect causes instability in the system and impacts mechanical components. In this paper, first, the governing equations of the problem and the system response have been obtained by considering the effects of shear deformations, as well as internal and external damping, in an overhung shaft-disk system. Then, using the instantaneous power balance method in the complex form, the occurrence of the Sommerfeld phenomenon has been investigated based on the Timoshenko beam theory. Another innovation is the utilization of numerical solutions and stability graph analysis to prevent complicated calculations and facilitate the determination of the Sommerfeld effect. In order to validate the obtained results, the problem was simulated using ABAQUS software whereby it was observed that the findings obtained from finite element analysis are in good agreement with our results. In addition to considering various mechanical effects such as shear deformation, gyroscopic effects, area moment, and internal damping, the proposed method allows studying the Sommerfeld effect in similar systems, with thick shafts.