A finite element model for stability analysis of symmetrical rotor systems with internal damping

Forrai, László (2000) A finite element model for stability analysis of symmetrical rotor systems with internal damping. JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS, 1 (1). pp. 37-47. ISSN 1586-2070

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Abstract

This paper deals with the stability analysis of self-excited bending vibrations of linear symmetrical rotor-bearing systems with internal damping using the finite element method. The rotor system consists of uniform circular Rayleigh shafts with internal viscous damping, symmetric rigid disks, and discrete isotropic damped bearings. The effect of rotatory inertia and gyroscopic moment are also included in the mathematical model. By combining the sensitivity analysis and the eigenvalue problem of the rotor dynamics equations presented in complex form, it is proved theoretically that the whirling motion of the rotor system becomes unstable at all speeds beyond the threshold speed of instability. In addition, the latter is always greater than the corresponding whirling speed. It is found that the rotor stability is improved by increasing the damping provided by the bearings, whereas increasing internal damping may reduce the stability threshold. It is also shown that the whirling speed of the rotor is higher than the first forward critical speed. Numerical examples are given to confirm the validity of the theoretical results.

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