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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

An Improved Transfer Matrix Method for Steady-State Analysis of Nonlinear Rotor-Bearing Systems

[+] Author and Article Information
J. W. Zu, Z. Ji

Department of Mechanical and Industrial Engineering, University of Toronto, Five King’s College Road, Toronto, ON M5S 3G8, Canada

J. Eng. Gas Turbines Power 124(2), 303-310 (Mar 26, 2002) (8 pages) doi:10.1115/1.1447235 History: Received February 01, 1998; Revised October 01, 2001; Online March 26, 2002
Copyright © 2002 by ASME
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References

Yamamoto,  T., Ishida,  Y., Ikedam,  T., and Yamada,  M., 1981, “Subharmonic and Summed-and-Differential Harmonic Oscillations of an Unsymmetrical Rotor,” Bull. JSME, 24, pp. 192–199.
Ishida,  Y., Ikeda,  T., and Yamamoto,  T., 1990, “Nonlinear Forced Oscillations Caused by Quadratic Nonlinearity in a Rotating Shaft,” ASME J. Vibr. Acoust., 112, pp. 288–297.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, John Wiley and Sons, New York, pp. 59–61.
Yamamoto,  T., Ishida,  Y., and Aizawa,  K., 1979, “On the Subharmonic Oscillations at Unsymmetrical Shafts,” Bull. JSME, 22, pp. 164–173.
Yamamoto,  T., Ishida,  Y., Ikeda,  T., and Yamamoto,  M., 1982, “Nonlinear Forced Oscillations of a Rotation Shaft Carrying on Unsymmetrical Rotor at the Major Critical Speed,” Bull. JSME, 25, pp. 1969.
Prohl,  M. A., 1945, “A General Method for Calculating Critical Speeds of Flexible Rotors,” ASME J. Appl. Mech., 67, p. 142.
Lund,  J. W., 1974, “Stability and Damped Critical Speeds of a Flexible Rotor in Fluid-Film Bearings,” J. Eng. Ind., 96, p. 509.
Gu,  J., 1986, “An Improved Transfer Matrix-Direct Integration Method for Rotor Dynamics,” ASME J. Vibr. Acoust., 108, pp. 182–188.
Lee,  A. C., Kang,  Y., and Liu,  S. L., 1991, “A Modified Transfer Matrix for the Linear Rotor-Bearing System,” ASME J. Appl. Mech., 58, pp. 776–783.
Kang,  Y., Lee,  A. C., and Shih,  Y. P., 1994, “A Modified Transfer Matrix Method for Asymmetric Rotor-Bearing Systems,” ASME J. Vibr. Acoust., 116, pp. 309–317.
Lee,  A. C., Kang,  Y., and Liu,  S. L., 1993, “Steady-State Analysis of a Rotor Mounted on Nonlinear Bearings by the Transfer Matrix Method,” Int. J. Mech. Sci., 35, pp. 479–490.
Zu,  J. W. and Han,  R. P. S., 1994, “Dynamic Response of a Spinning Timoshenko Beam With General Boundary Conditions and Subjected to a Moving Load,” ASME J. Appl. Mech., 61, pp. 152–160.
Zu,  J. W. and Ji,  Z. Y., 1998, “Steady-State Response of Rotor Systems With Timoshenko shaft and Nonlinear Bearings,” ASME J. Eng. Gas Turbines Power, 120, pp. 751–758.

Figures

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A shaft-bearing system with divided elements
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A flowchart of solution scheme
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A shaft-bearing system with an intermediate rotor
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Frequency response for various K3
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Whirling orbit at point B for K3=1.0e1 1N/cm3 and Ω=78.8 rad/s
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Frequency response at K3=1.0e9N/cm3
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A shaft-bearing system with multiple bearings and disks
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Frequency response for various K3
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Whirling orbits at point B for K3=1.0e1 6N/m3 and Ω=96 rad/s

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