Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] A. S. Besicovitch, Almost periodic functions, Cambridge University Press, Cambridge, 1932
  • [2] E. Oran Brigham, The Fast Fourier Transform, Prentice Hall, Englewood Cliffs, 1974
  • [3] 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)
  • [4] 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)
  • [5] Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
  • [6] R. A. Collacott, Vibration monitoring and diagnosis, John Wiley & Sons, New York, 1979
  • [7] W. B. Day, Asymptotic expansions in nonlinear rotordynamics, Quart. Appl. Math. 44, 779-792 (1987)
  • [8] 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)
  • [9] Jack K. Hale, Ordinary differential equations, 2nd ed., Robert E. Krieger Publishing Co., Inc., Huntington, N.Y., 1980. MR 587488
  • [10] 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)
  • [11] B. F. Rowan, Rotordynamics technical manual, Rockwell International, Rocketdyne Division, Canoga Park, California, November 1981
  • [12] T. T. Yamamoto, On critical speeds of a shaft, Mem. Fac. Engr. Nagoya Univ. 6, 106-174 (1954)

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Additional Information

DOI: https://doi.org/10.1090/qam/1031678
Article copyright: © Copyright 1989 American Mathematical Society


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