The behavior of linear rotor-bearing systems is investigated by using the exact approach of the dynamic stiffness method, which entails the use of continuous rather than lumped models. In particular, the theoretical formulation for rotor systems with anisotropic bearings is developed by utilizing the complex representation of all the involved variables. The proposed formulation eventually leads to the 8 × 8 complex dynamic stiffness matrix of the rotating Timoshenko beam; this matrix proves to be related, by a simple rule, to the 4 × 4 dynamic stiffness matrix, which describes rotor systems with isotropic bearings. The method is first applied to the critical speeds evaluation of a simple rotor system with rigid supports; for this case, the exact results of the dynamic stiffness approach are compared to the usual convergence procedure of the finite element method. Successively, the steady-state unbalance response of two rotor systems with anisotropic supports is analyzed; for these examples, the dynamic stiffness results compare favorably with the results of the finite element and the transfer matrix analysis performed by other authors.

1.
AFAPL-TR-78-6, 1980, “Rotor-Bearing Dynamics Technology Design Guide,” Part 1-Flexible Rotor Dynamics.
2.
Cook, R. D., 1981, Concepts and Applications of Finite Element Analysis, 2nd ed., John Wiley & Sons.
3.
Cossalter, V., and Da Lio, M., 1986, “Un Codice per l’Analisi Dinamica di Sistemi Rotore-Cuscinetti-Struttura Portante,” II Progettista Industriale, No. 9, pp. 80–90.
4.
Curti
G.
,
Raffa
F. A.
, and
Vatta
F.
,
1992
, “
An Analytical Approach to the Dynamics of Rotating Shafts
,”
Meccanica
, Vol.
27
, pp.
285
292
.
5.
Curti, G., Raffa, F. A., and Vatta, F., 1993a, “Externally Damped Rotor Systems by the Dynamic Stiffness Method,” Proceedings, 11th International Modal Analysis Conference, Orlando, FL, Vol. I, pp. 538–544.
6.
Curti, G., Raffa, F. A., and Vatta, F., 1993b, “Steady-State Unbalance Response of Continuous Rotors on Anisotropic Supports,” Proceedings, 14th ASME Biennial Conference on Mechanical Vibration & Noise, Albuquerque, NM, DE-Vol. 60, pp. 27–34.
7.
Dimentberg, F. M., 1961, Flexural Vibrations of Rotating Shafts, Butterworths, London.
8.
Kikuchi
K.
,
1970
, “
Analysis of Unbalance Vibration of Rotating Shaft System with Many Bearings and Disks
,”
Bulletin of the JSME
, Vol.
13
, pp.
864
872
.
9.
Lee
A.-C.
,
Kang
Y.
, and
Liu
S.-L.
,
1991
, “
A Modified Transfer Matrix Method for Linear Rotor-Bearing Systems
,”
ASME Journal of Applied Mechanics
, Vol.
58
, pp.
776
783
.
10.
Lund
J. W.
, and
Orcutt
F. K.
,
1967
, “
Calculations and Experiments on the Unbalance Response of a Flexible Rotor
,”
ASME Journal of Engineering for Industry
, Vol.
89
, pp.
785
796
.
11.
Myklestad
N. O.
,
1944
, “
A New Method of Calculating Natural Modes of Uncoupled Bending Vibration of Airplane Wings and Other Types of Beams
,”
Journal of the Aeronautical Sciences
, Vol.
11
, pp.
153
162
.
12.
Nelson
H. D.
, and
McVaugh
J. M.
,
1976
, “
The Dynamics of Rotor-Bearing Systems Using Finite Elements
,”
ASME Journal of Engineering for Industry
, Vol.
98
, pp.
593
600
.
13.
Nelson, H. D., and Meacham, W. L., 1981, “Transient Analysis of Rotor Bearing Systems using Component Mode Synthesis,” ASME Paper No. 81-GT-110.
14.
Nevzat O¨zgu¨ven
H.
, and
Levent O¨zkan
Z.
,
1984
, “
Whirl Speeds and Unbalance Response of Multibearing Rotors using Finite Elements
,”
ASME JOURNAL OF VIBRATION, ACOUSTICS, STRESS, AND RELIABILITY IN DESIGN
, Vol.
106
, pp.
72
79
.
15.
Prohl
M. A.
,
1945
, “
A General Method for Calculating Critical Speeds of Flexible Rotors
,”
ASME Journal of Applied Mechanics
, Vol.
67
, pp.
A142–A148
A142–A148
.
16.
Rieger, N. F., Thomas, C. B., and Walter, W. W., 1976, “Dynamic Stiffness Matrix Approach for Rotor-Bearing System Analysis,” Proceedings, IMechE Conference Vibration in Rotating Machinery, Paper C187/76, pp. 187–190.
17.
Smirnov, V. I., 1979, Corso di Matematica Superiore, Vol. I, Editori Riuniti, Roma.
18.
Thomas, C. B., 1974, “A Unified Formulation for the Unbalance Response of a Flexible Rotor in Fluid-Film Bearings,” Master Thesis, Rochester Institute of Technology, Rochester, New York.
This content is only available via PDF.
You do not currently have access to this content.