In this paper, the rotating flexible-Timoshenko-shaft/flexible-disk coupling system is formulated by introducing the kinetic and strain energies, and the virtual work done by the eddy-current brake system into Hamilton’s principle. The attachment of disk to shaft becomes flexible for Timoshenko-beam theory and rigid for Euler-beam theory. It is found that the eddy-current brake system can be used to decrease speed and suppress flexible and shear vibrations simultaneously. From the dynamic formulations and energy analysis, some important discussions are made. Numerical results are provided to validate the theoretical analysis. [S0739-3717(00)01504-X]
Issue Section:
Technical Papers
1.
Simmonds
, J. G.
, 1962
, “The Transverse Vibrations of a Flat Spinning Membrane
,” J. Aeronaut. Sci.
, 29
, No. 1
, pp. 16
–18
.2.
Simmonds
, J. G.
, 1963
, “Axisymmetric, Transverse Vibrations of a Spinning Membrane Clamped at Its Center
,” AIAA J.
, 1
, No. 5
, pp. 1224
–1225
.3.
Eversman
, W.
, 1968
, “Transverse Vibrations of a Clamped Spinning Membrane
,” AIAA J.
, 6
, No. 7
, pp. 1395
–1397
.4.
Choi
, S. H.
, Pierre
, C.
, and Ulsoy
, A. G.
, 1992
, “Consistent Modeling of Rotating Timoshenko Shafts Subject to Axial Loads
,” Trans. ASME, J. Vib., Acoust., Stress
, 114
, pp. 249
–259
.5.
Vance, J. M., 1988, Rotordynamics of Turbomachinery, Wiley, New York.
6.
Sankar
, T. S.
, 1991
, “Rotor Dynamics: A State-of-the Art
,” Trans. Can. Soc. Mech. Eng.
, 150
, No. 1
, pp. 1
–42
.7.
Ehrich, F. F., ed., 1992, Handbook of Rotordynamics, McGraw-Hill, New York.
8.
Shahab
, A. A. S.
, and Thomas
, J.
, 1987
, “Coupling Effects of Disc Flexibility on the Dynamic Behavior of Multi Disc-Shaft Systems
,” J. Sound Vib.
, 114
, No. 3
, pp. 435
–452
.9.
Sakata
, M.
, Kimura
, K.
, Park
, S. K.
, and Ohnabe
, H.
, 1989
, “Vibration of Bladed Flexible Rotor due to Gyroscopic Moment
,” J. Sound Vib.
, 131
, No. 3
, pp. 417
–430
.10.
Wu
, F.
, and Flower
, G. T.
, 1992
, “A Transfer Matrix Technique for Evaluating the Natural Frequencies and Critical Speeds of a Rotor With Multiple Flexible Disks
,” ASME J. Vibr. Acoust.
, 114
, pp. 242
–248
.11.
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
, No. 5
, pp. 587
–608
.12.
Lee
, C. W.
, Jia
, H. S.
, Kim
, C. S.
, and Chun
, S. B.
, 1997
, “Tuning of Simulated Natural Frequencies for a Flexible Shaft-Multiple Flexible Disk System
,” J. Sound Vib.
, 207
, No. 4
, pp. 435
–451
.13.
Lee
, C. W.
, and Chun
, S. B.
, 1998
, “Vibration Analysis of a Rotor With Multiple Flexible Disks Using Assumed Modes Method
,” Trans. ASME, J. Vib., Acoust., Stress
, 120
, pp. 87
–94
.14.
Nagaya
, K.
, and Kojima
, H.
, 1984
, “On a Magnetic Damper Consisting of a Circular Magnetic Flux and a Conductor of Arbitrary Shape. Part I: Derivation of the Damping Coefficients
,” ASME J. Dyn. Syst., Meas., Control
, 106
, pp. 46
–51
.15.
Nagaya
, K.
, 1984
, “On a Magnetic Damper Consisting of a Circular Magnetic Flux and a Conductor of Arbitrary Shape. Part II: Applications and Numerical Results
,” ASME J. Dyn. Syst., Meas., Control
, 106
, pp. 52
–56
.16.
Wiederick
, H. D.
, Gauthier
, N.
, Campbell
, D. A.
, and Rochon
, P.
, 1987
, “Magnetic Braking: Simple Theory and Experiment
,” Am. J. Phys.
, 55
, No. 6
, pp. 500
–503
.17.
Heald
, M. A.
, 1998
, “Magnetic Braking: Improved Theory
,” Am. J. Phys.
, 56
, No. 6
, pp. 521
–522
.18.
Wouterse
, J. H.
, 1991
, “Critical Torque and Speed of Eddy Current Brake with Widely Separated Soft Iron Poles
,” IEE Proc B
, 138
, No. 4
, pp. 153
–158
.19.
Cadwell
, L. H.
, 1996
, “Magnetic Damping: Analysis of an Eddy Current Brake Using an Airtrack
,” Am. J. Phys.
, 64
, No. 7
, pp. 971
–923
.20.
Reismann, H., and Pawlik, P. S., 1980, Elasticity: Theory and Applications, Wiley, New York.
21.
Reismann, H., 1988, Elastic Plates: Theory and Application, Wiley, New York.
22.
Ugural, A. C., and Fenster, S. K., 1981, Advanced Strength and Applied Elasticity, Elsevier, New York.
23.
Meirovitch, L., 1989, Dynamics and Control of Structures, Wiley, New York.
24.
Jia
, H. S.
, 1999
, “On the Bending Coupled Natural Frequencies of a Spinning, Multispan Timoshenko Shaft Carrying Elastic Disks
,” J. Sound Vib.
, 221
, No. 4
, pp. 623
–649
.25.
Lee
, H. P.
, 1995
, “Dynamic Response of A Rotating Timoshenko Shaft Subject to Axial Forces and Moving Loads
,” J. Sound Vib.
, 181
, No. 1
, pp. 169
–177
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