Keywords: flexible rotor, multi-bearing rotors, spectral element model, critical speed, dynamic behaviour, finite element model.

The rotator systems consist of multiple shafts, disks and multiple bearings. As it is very important to predict the dynamic characteristics of the rotor systems accurately in the early design phase, much effort also has been given to the development of solution methods for rotor dynamics during the past many decades. The finite element method (FEM) became available in the 1970s for the solution of the prevailing beam-based rotor models [1]. Though the FEM is certainly a powerful solution technique for rotor systems, it is often inevitable to use the finer meshes especially at high frequency to improve the accuracy of FEM solutions, which will drastically increase the computation cost. Thus, as an alternative of the FEM, this paper introduces the spectral element method (SEM).

The SEM is a frequency-domain solution method where the spectral element matrix formulated from exact wave solutions is used as the dynamic stiffness matrix. Thus, in contrast to the FEM, one-element representation is sufficient to investigate exact dynamic behaviour a continuum system, regardless of its dimension, in the absence of any geometrical or material discontinuity. This may significantly reduce the computation cost as a by-product [2,3]

Motivated from the advantages of SEM, this paper presents a spectral element model for the flexible rotor systems with thin rigid disks. The spinning circular shafts of a rotor system are represented by the uniform Timoshenko beam models and the disks are considered to be wobbling about their centres. The bearings are regarded as the flexible bearings and represented by translational and rotational springs. The mass unbalances of disks are taken into account in the spectral element model. The spectral element model is then applied to some example rotor systems and the numerical results obtained by using the present spectral element model are compared with those obtained by using the conventional FEM as well as with those cited from existing references. It is shown that the present spectral element model provides very accurate results for all example problems considered in this paper.

1

R.L. Ruhl, J.F. Booker, "A Finite Element for Distributed Parameter Turborotor Systems", Journal of Engineering for Industry, 94, 126-132, 1972.

2

U. Lee, J. Kim, A.Y.T. Leung, "The Spectral Element Method in Structural Dynamics", The Shock and Vibration Digest, 32(6), 451-465, 2000. doi:10.1177/058310240003200601

3

U. Lee, "Spectral Element Method in Structural Dynamics", Inha University Press, Inha University, Incheon, Korea, 2004.

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