Distributed Parameter Rotor-Bearing Systems

  • Chong-Won Lee
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 21)


The transverse vibration of rotor systems with distributed mass becomes an important issue when one needs to gain deep insight into the dynamic behavior of rotor systems. As far as the equations of motion are concerned, the complexity of the analysis increases as the rotary inertia [1,2], gyroscopic moments [3], shear deformation [4,5] and their combined effects [6,7] are taken into account. Regardless of the complexity introduced in rotor models, the resonant frequency, critical speed calculations and stability analysis are relatively straightforward. However, the mode shapes associated with the natural frequencies and thus the forced response analysis(modal analysis) of distributed mass rotor systems with the added complexity are not readily available except in the extremely simple case of an Euler-Bernoulli rotor model(without the gyroscopic terms) [1,8]. It has already been pointed out in the previous chapters that the Euler-Bernoulli rotor model is not a suitable model for investigating those aspects of rotor systems which distinguish them from ordinary structures. The difficulties in modal analysis of rotor systems arise from the fact that their eigenvalue problems are characterized by the presence of skew symmetric matrices with differential operators as elements due to rotation and/or damping, leading to non-self-adjoint eigenvalue problems [9].


Modal Frequency Modal Analysis Mode Shape Vibration Analysis Rotor System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. E. D. Bishop, “On the Possibility of Balancing Rotating Flexible Shafts,” J. Mech. Eng. Sci., Vol. 24, No. 4, 1982, p. 215–220.CrossRefGoogle Scholar
  2. 2.
    Y. D. Kim and C. W. Lee, “Determination of the Optimal Balancing Head Location on Flexible Rotors Using a Structural Dynamics Modification Algorithm,” Proc. Instn. Mech. Engrs., Vol.199, No. C1, 1985, p. 19–25.Google Scholar
  3. 3.
    R.B. Green, “Gyroscopic Effects on the Critical Speeds of Flexible Rotors,” J. Applied Mechanics, 15, 1948, p. 369–374.Google Scholar
  4. 4.
    F.M. Dimentberg, Flexural Vibrations of Rotating Shafts, London: Butterworth, 1961.Google Scholar
  5. 5.
    T.C. Huang and F.C.C. Huang, “On Precession and Critical Speeds of Two-Bearing Machines with Overhung Weight,” J. Eng. for Industry, Vol. 89, 1967, p. 713–718.CrossRefGoogle Scholar
  6. 6.
    R.L. Eshleman and R.A. Eubanks, “On the Critical Speeds of Continuous Rotor,” J. Eng. for Industry, Vol. 91, 1969, p. 1180–1188.CrossRefGoogle Scholar
  7. 7.
    I. Porat and M. Niv, “Vibrations of a Rotating Shaft by the Timoshenko Beam Theory,” Israel Journal of Technology, 1971, p. 535–546.Google Scholar
  8. 8.
    G.M.L. Gladwell and R.E.D. Bishop, “The Vibration of Rotating Shafts Supported in Flexible Bearings,” J. Mech. Eng. Sci., Vol. 1, 1959, p. 195–206.zbMATHCrossRefGoogle Scholar
  9. 9.
    L. Meirovitch and L.M. Silverberg, “Control of Non-Self-Adjoint Distributed-Parameter Systems,” J. Optimization Theory and Applications, Vol. 47, 1985, p. 77–90.MathSciNetCrossRefGoogle Scholar
  10. 10.
    C. W. Lee and Y. G. Jei, “Modal Analysis of Continuous Rotor-Bearing Systems,” J. Sound and Vibration, Vol. 126, No. 2, 1988, p. 345–361.CrossRefGoogle Scholar
  11. 11.
    Y. G. Jei and C. W. Lee, “Vibrations of Anisotropic Rotor-Bearing Systems,” Twelfth Biennial ASME Conference on Mechanical Vibration and Noise, Montreal, Canada, September 1989.Google Scholar
  12. 12.
    Y. G. Jei and C. W. Lee, “Modal Analysis of Continuous Asymmetrical Rotor-Bearing Systems,” J. Sound and Vibration, Vol. 152, No. 2, 1992, p. 245–262.zbMATHCrossRefGoogle Scholar
  13. 13.
    C. W. Lee, R. Katz, A. G. Ulsoy, and R. A. Scott, “Modal Analysis of a Distributed Parameter Rotating Shaft,” J. Sound and Vibration, Vol. 122, No. 1, 1988, p. 119–130.CrossRefGoogle Scholar
  14. 14.
    R. Katz, C.W. Lee, A.G. Ulsoy and R.A. Scott, “The Dynamic Response of a Rotating Shaft Subject to a Moving Load,” J. Sound and Vibration, Vol. 122, No. 1, 1988, p. 131–148.CrossRefGoogle Scholar
  15. 15.
    P. Lancaster, Lambda Matrices and Vibrating Systems, Pergamon Press, 1966.Google Scholar
  16. 16.
    R. Nordmann, “Modal Analysis in Rotor Dynamics,” Chapter 1, Dynamics of Rotors: Stability and System Identification, edited by O. Mahrenholtz, Springer-Verlag, 1984.Google Scholar
  17. 17.
    L. Meirovitch, Computational Methods in Structural Dynamics, Rockville, Maryland: Sijthoff & Noordhoff, 1980.zbMATHGoogle Scholar
  18. 18.
    J. S. Kim and C. W. Lee, “Constrained Output Feedback Control of Flexible Rotor Bearing Systems,” J. Sound and Vibration, Vol. 138, No. 1, 1990, p. 95–114.CrossRefGoogle Scholar
  19. 19.
    J. E. Shigley, Mechanical Engineering Design, 3rd ed., McGraw-Hill, Inc., 1977.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • Chong-Won Lee
    • 1
  1. 1.Center for Noise and Vibration Control (NOVIC), Department of Mechanical EngineeringKorea Advanced Institute of Science and TechnologyTaejonKorea

Personalised recommendations