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TECHNICAL PAPERS

Ritz Series Analysis of Rotating Shaft System: Validation, Convergence, Mode Functions, and Unbalance Response

[+] Author and Article Information
Nicole L. Zirkelback, Jerry H. Ginsberg

G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405

J. Vib. Acoust 124(4), 492-501 (Sep 20, 2002) (10 pages) doi:10.1115/1.1501081 History: Received October 01, 2001; Revised April 01, 2002; Online September 20, 2002
Copyright © 2002 by ASME
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References

Bishop,  R. E. D., 1959, “The Vibration of Rotating Shafts,” J. Mech. Eng. Sci., 1, pp. 50–65.
Gladwell,  G. M. L., and Bishop,  R. E. D., 1959, “The Vibration of Rotating Shafts Supported in Flexible Bearings,” J. Mech. Eng. Sci., 1, pp. 195–206.
Morton,  P. G., 1965, “On the Dynamics of Large Turbo-Generator Rotors,” Proc. Inst. Mech. Eng., 180, Pt. (1), No 12, pp. 295–329.
Morton,  P. G., 1972, “Analysis of Rotors Supported Upon Many Bearings,” J. Mech. Eng. Sci., 14, pp. 25–33.
Black,  H. F., 1974, “Calculation of Forced Whirling and Stability of Centrifugal Pump Rotor Systems,” ASME J. Eng. Ind., 96, pp. 1076–1084.
Black, H. F., and Brown, R. D., 1980, “Modal Dynamic Simulation of Flexible Shafts in Hydrodynamic Bearings,” IMechE Conference Publications, Vibration in Rotating Machinery, pp. 109–113.
Shiau,  T. N., and Hwang,  J. L., 1989, “A New Approach to the Dynamic Characteristic of Undamped Rotor-Bearing Systems,” ASME J. Vibr. Acoust., 111, pp. 379–385.
Hwang,  J. L., and Shiau,  T. N., 1991, “An Application of the Generalized Polynomial Expansion Method to Nonlinear Rotor Bearing Systems,” ASME J. Vibr. Acoust., 113, pp. 299–308.
Shiau,  T. N., and Hwang,  J. L., 1993, “Generalized Polynomial Expansion Method for the Dynamic Analysis of Rotor-Bearing Systems,” ASME J. Eng. Gas Turbines Power, 115, pp. 209–217.
Shiau,  T. N., Hwang,  J. L., and Chang,  Y. B., 1993, “A Study on Stability and Response Analysis of a Nonlinear Rotor System with Mass Unbalance and Side Load,” ASME J. Eng. Gas Turbines Power, 115, pp. 218–226.
Lee,  H. P., 1993, “Divergence of a Rotating Shaft with an Intermediate Support and Conservative Axial Loads,” Comput. Methods Appl. Mech. Eng., 110, pp. 317–324.
Lee,  H. P., 1994, “Dynamic Stability of Spinning Pre-Twisted Beams,” International Journal of Solids and Structures , 31 (18), pp. 2509–2517.
Lee,  H. P., 1996, “Dynamic Stability of Spinning Beams of Unsymmetrical Cross-Section with Distinct End Conditions,” J. Sound Vib., 189 (2), pp. 161–171.
Chun,  S.-B., and Lee,  C.-W., 1996, “Vibration Analysis of Shaft-Bladed Disk System by Using Substructure Synthesis and Assumed Modes Method,” J. Sound Vib., 189 (5), pp. 587–608.
Lee,  C.-W., and Chun,  S.-B., 1998, “Vibration Analysis of a Rotor with Multiple Flexible Disks Using Assumed Modes Method,” ASME J. Vibr. Acoust., 120, pp. 87–94.
Hamidi,  L., Piaud,  J. B., Pastorel,  H., Mansour,  W. M., and Massoud,  M., 1994, “Modal Parameters for Cracked Rotors: Models and Comparisons,” J. Sound Vib., 175 (2), pp. 265–286.
Singh,  S. P., and Gupta,  K., 1996, “Composite Shaft Rotordynamic Analysis Using a Layerwise Theory,” J. Sound Vib., 191 (5), pp. 739–756.
Fung,  R.-F., and Hsu,  S.-M., 2000, “Dynamic Formulations and Energy Analysis of Rotation Flexible-Shaft/Multi-Flexible-Disk System with Eddy-Current Brake,” ASME J. Vibr. Acoust., 122, pp. 365–375.
Zirkelback, N. L., and Ginsberg, J. H., 2001, “Ritz Series Analysis of Rotating Machinery Incorporating Timoshenko Beam Theory,” ASME Paper 2001-GT-244.
Lee, C.-W., 1993, Vibration Analysis of Rotors, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Ginsberg, J. H., 2001, Mechanical and Structural Vibrations: Theory and Applications, Wiley, New York.
Childs, D., 1994, Turbomachinery Rotordynamics, John Wiley and Sons, Inc., New York.
Kim,  Y. D., and Lee,  C. W., 1986, “Finite Element Analysis of Rotor Bearing Systems Using a Modal Transformation Matrix,” J. Sound Vib., 111 (3), pp. 441–456.
Ehrich, F. F, ed., 1999, Handbook of Rotordynamics, Krieger Publishing Company, Inc., Malibar, FL.

Figures

Grahic Jump Location
Relationships between axes and rotations for a differential shaft element
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Overhung rotor system with two bearings in 20. κ=2,738,τ=0.0016,μd=0.4775,rP=0.07303,rT=0.05164,kyy=407.4,kzz=651.9,cyy=czz=5.093.
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Critical speed map with a 1X synchronous line for an overhung rotor bearing system. Comparison with the finite element method in 20.
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Rezoning convergence study. Markers denote critical speed number.
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Convergence study with generalized coordinates qj
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Mode function magnitudes and phase angles in terms of elliptical parameters (a,b, and θ) for the first and second critical speeds
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Mode function magnitudes and phase angles in terms of elliptical parameters (a,b, and θ) for the third and fourth critical speeds
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Mode function magnitudes and phase angles in terms of elliptical parameters (a,b, and θ) for the fifth and sixth critical speeds
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Unbalance response magnitudes and phase angles for displacements v and w

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