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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

Reduced-Order Nonlinear Dynamic Model of Coupled Shaft-Torsional and Blade-Bending Vibrations in Rotors

[+] Author and Article Information
B. O. Al-Bedoor

Mechanical Engineering Department, King Fahd University of Petroleum & Minerals, KFUPM Box 841, Dhahran 31261, Saudi Arabia

J. Eng. Gas Turbines Power 123(1), 82-88 (May 16, 2000) (7 pages) doi:10.1115/1.1341203 History: Received April 28, 2000; Revised May 16, 2000
Copyright © 2001 by ASME
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References

Shilahansi,  L., 1958, “Bending Frequencies of a Rotating Cantilever Beam,” ASME J. Appl. Mech., 25, pp. 28–30.
Pruelli,  D., 1972, “Natural Bending Frequency Comparable to Rotational Frequency in Rotating Cantilever Beam,” ASME J. Appl. Mech., 39, pp. 602–604.
Likins,  P. W., Barbera,  F. J., and Baddeley,  V., 1973, “Mathematical Modeling of Spinning Elastic Bodies,” AIAA J., 11, No. 9, pp. 1251–1258.
Kaza,  K., and Kvaternik,  R., 1977, “Nonlinear Flap-Lag-Axial Equations of a Rotating Beam,” AIAA J., 15, No. 6, pp. 871–874.
Yokoyama,  T., 1988, “Free Vibration Characteristics of Rotating Timoshenko Beams,” Int. J. Mech. Sci., 30, No. 10, pp. 743–755.
Al-Bedoor,  B. O., and Khulief,  Y., 1997, “General Planar Dynamics of a Sliding Flexible Link,” J. Sound Vib., 206, No. 5, pp. 641–661.
Srinivasan,  A. V., 1984, “Vibrations of Bladed-Disk Assemblies: A Selected Survey,” ASME J. Vibr. Acoust., 106, pp. 165–168.
Crawley,  E., and Mokadam,  D., 1984, “Stager Angle Dependence of the Inertial and the Elastic Coupling in Bladed Disks,” ASME J. Vibr. Acoust., 106, pp. 181–188.
Tang,  D., and Wang,  M., 1984, “Coupling Technique of Rotor-Fuselage Dynamic Analysis,” ASME J. Vibr. Acoust., 106, pp. 235–238.
Loewy,  R. G., and Khader,  N., 1984, “Structural Dynamics of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft Motions,” AIAA J., 22, No. 9, pp. 1319–1327.
Crawley,  E. F., Ducharme,  E., and Mokadam,  D., 1986, “Analytical and Experimental Investigation of the Coupled Bladed Disk Shaft Whirl of a Cantilever Turbofan,” ASME J. Eng. Gas Turbines Power, 108, pp. 567–576.
Okabe,  A., Otawara,  Y., Kaneko,  R., Matsushita,  O., and Namura,  K., 1991, “An Equivalent Reduced Modeling Method and Its Application to Shaft-Blade Coupled Torsional Vibration Analysis of a Turbine-Generator Set,” Proc. Inst. Mech. Eng., 205, pp. 173–181.
Huang,  S. C., and Ho,  K. B., 1996, “Coupled Shaft-Torsion and Blade-Bending Vibrations of a Rotating Shaft-Blade Unit,” ASME J. Eng. Gas Turbines Power, 118, pp. 100–106.
Al-Bedoor,  B. O., 1998, “Vibrations of a Rotating Blade With Flexible Coupling in the Drive System,” ASME Pressure Vessels Piping, PVP, 368, pp. 69–76.
Szabelski,  K., and Warminski,  J., 1995, “Parametric Self-Excited Nonlinear System Vibration Analysis With Inertial Excitation,” Int. J. Nonlinear Mech., 30, No. 2, pp. 179–189.

Figures

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Schematic diagram of blade-disk-shaft system
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System deformed configuration and coordinate system
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Motor torque to rotate the system to a speed of 1000 RPM in 1 sec
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(a) Blade deflection and (b) frequency spectrum
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Coupling torsional deflection
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Blade first bending mode vibrations
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Blade second bending mode vibrations
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Blade third bending mode vibrations
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Blade fourth bending mode vibrations
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Blade fifth bending mode vibrations

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