Stability and modal analysis of an unbalanced asymmetric multi-disk rotor system on bearings as viscoelastic substrate

• Published in: Archive of applied mechanics (1991) Vol. 92; no. 8; pp. 2247 - 2271
• Main Authors: Tarkashvand, A., Golmohammadi, A., Safizadeh, M. S.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2022; Springer Nature B.V
• Subjects: Asymmetry; Beam theory (structures); Bearings; Classical Mechanics; Damper bearings; Damping; Disks; Engineering; Exact solutions; Forced vibration; Free vibration; Frequency response; Frequency stability; Mathematical models; Modal analysis; Original; Resonant frequencies; Rotary inertia; Rotors; Shear deformation; Springs (elastic); Stability analysis; Stiffness; Substrates; Theoretical and Applied Mechanics; Timoshenko beams; Vibration analysis; Viscoelasticity; Stability analysis; Timoshenko beam theory; Viscoelastic substrate; Modal analysis; Multi-disk rotor system
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-022-02176-4

In the present work, an exact analytical solution is presented to investigate the frequency response and stability of a very complex asymmetric rotor-disk-bearing system considering the shear deformation and rotary inertia despite the unbalance. The system consists of eighteen disks, a rotor, and three bearings, and all components of the system are considered elastic. Also, disks are modeled as Timoshenko beam elements and in fact, their bending flexibility is considered. But, because of their high ratios of diameter to length of them, they are practically rigid in the presented model. Here the bearings are modeled with springs and dampers. In other words, the rotor-disk system is assumed to be on oil-lubricated bearings as viscoelastic supports. Timoshenko's beam theory based on the Hamiltonian principle is used to derive governing equations of the problem. Then, to confirm the equations, the results were compared with those obtained by other researchers, and a good agreement was found. The natural frequencies of the rotor-disk-bearing system were also obtained in the free vibration case and the orbit shapes were then plotted according to each frequency. Finally, the influences of different parameters including bearing stiffness and damping, internal damping of structure, mass unbalance for forced vibration case on displacement amplitude and rotation were analyzed.