The Jeffcott equations in nonlinear rotordynamics
Author:
R. A. Zalik
Journal:
Quart. Appl. Math. 47 (1989), 585-599
MSC:
Primary 70K40; Secondary 34A30, 70K20, 73H10, 73K12
DOI:
https://doi.org/10.1090/qam/1031678
MathSciNet review:
MR1031678
Full-text PDF Free Access
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Abstract: The Jeffcott equations are a system of coupled differential equations that represent the behavior of a rotating shaft. This is a simple model that allows investigation of the basic dynamic behavior of rotating machinery. Nonlinearities can be introduced by taking into consideration deadband, side force, and rubbing, among others.
A. S. Besicovitch, Almost periodic functions, Cambridge University Press, Cambridge, 1932
E. Oran Brigham, The Fast Fourier Transform, Prentice Hall, Englewood Cliffs, 1974
D. W. Childs, The space shuttle main engine high-pressure fuel turbopump rotordynamics instability problem, Trans. ASME, J. Engineering for Power, 48–57 (January 1978)
Y. S. Choi and S. T. Noah, Nonlinear steady-state response of a rotor-support system, Trans. ASME, J. Vibration, Acoustics, Stress and Reliability in Design 109, 255–261 (1987)
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
R. A. Collacott, Vibration monitoring and diagnosis, John Wiley & Sons, New York, 1979
W. B. Day, Asymptotic expansions in nonlinear rotordynamics, Quart. Appl. Math. 44, 779–792 (1987)
P. K. Gupta, L. W. Winn, and D. B. Wilcock, Vibrational characteristics of ball bearings, Trans. ASME, J. of Lubrication Technology 99F, No. (2), 284–289 (1977)
- Jack K. Hale, Ordinary differential equations, 2nd ed., Robert E. Krieger Publishing Co., Inc., Huntington, N.Y., 1980. MR 587488
H. H. Jeffcott, The lateral vibration of loaded shafts in the neighborhood of a whirling speed—The effect of want of balance, Philos. Mag. Ser. 6, 37, 304–314 (1919)
B. F. Rowan, Rotordynamics technical manual, Rockwell International, Rocketdyne Division, Canoga Park, California, November 1981
T. T. Yamamoto, On critical speeds of a shaft, Mem. Fac. Engr. Nagoya Univ. 6, 106–174 (1954)
A. S. Besicovitch, Almost periodic functions, Cambridge University Press, Cambridge, 1932
E. Oran Brigham, The Fast Fourier Transform, Prentice Hall, Englewood Cliffs, 1974
D. W. Childs, The space shuttle main engine high-pressure fuel turbopump rotordynamics instability problem, Trans. ASME, J. Engineering for Power, 48–57 (January 1978)
Y. S. Choi and S. T. Noah, Nonlinear steady-state response of a rotor-support system, Trans. ASME, J. Vibration, Acoustics, Stress and Reliability in Design 109, 255–261 (1987)
E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw Hill, 1955 (Reprint, Robert E. Krieger Publishing Co., Malabar, Florida, 1984)
R. A. Collacott, Vibration monitoring and diagnosis, John Wiley & Sons, New York, 1979
W. B. Day, Asymptotic expansions in nonlinear rotordynamics, Quart. Appl. Math. 44, 779–792 (1987)
P. K. Gupta, L. W. Winn, and D. B. Wilcock, Vibrational characteristics of ball bearings, Trans. ASME, J. of Lubrication Technology 99F, No. (2), 284–289 (1977)
J. K. Hale, Ordinary differential equations, 2nd ed., Robert E. Krieger Publishing Co., Malabar, Florida, 1980
H. H. Jeffcott, The lateral vibration of loaded shafts in the neighborhood of a whirling speed—The effect of want of balance, Philos. Mag. Ser. 6, 37, 304–314 (1919)
B. F. Rowan, Rotordynamics technical manual, Rockwell International, Rocketdyne Division, Canoga Park, California, November 1981
T. T. Yamamoto, On critical speeds of a shaft, Mem. Fac. Engr. Nagoya Univ. 6, 106–174 (1954)
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Article copyright:
© Copyright 1989
American Mathematical Society
