A model for the in-plane oscillations of a thin rotating disk has been derived using a nonlinear strain measure to calculate the disk energy. This accounts for the stiffening of the disk due to the radial expansion resulting from its rotation. The corresponding nondimensionalized natural frequencies are seen to depend only on the nondimensionalized rotation speed and have been calculated. The radially expanded disk configuration is linearly stable over the range of rotation speeds studied here. The sine and cosine modes for all nodal diameters couple to each other at all non-zero rotation speeds and the strength of this coupling increases with rotation speed. This coupling causes the reported frequencies of the stationary disk to split. The zero, one and two nodal diameter in-plane modes do not have a critical speed corresponding to the vanishing of the backward travelling wave frequency. The use of a linear strain measure in earlier work incorrectly predicts instability of the rotating equilibrium and the existence of critical speeds in these modes.
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January 2003
Technical Papers
In-Plane Vibrations of a Thin Rotating Disk
Moreshwar Deshpande,
Moreshwar Deshpande
ZS Associates, 400 El Camino Real, #1500, San Mateo, CA 94402
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C. D. Mote,, Jr., President and Glenn L. Martin Institute Professor of Engineering
C. D. Mote,, Jr., President and Glenn L. Martin Institute Professor of Engineering
University of Maryland, College Park, MD 20742
Search for other works by this author on:
Moreshwar Deshpande
ZS Associates, 400 El Camino Real, #1500, San Mateo, CA 94402
C. D. Mote,, Jr., President and Glenn L. Martin Institute Professor of Engineering
University of Maryland, College Park, MD 20742
Contributed by the Technical Committee on Vibration and Sound for publication in the Journal of Vibration and Acoustics. Manuscript received Jan. 2000; Revised Dec. 2001. Associate Editor: R. P. S. Han.
J. Vib. Acoust. Jan 2003, 125(1): 68-72 (5 pages)
Published Online: January 6, 2003
Article history
Received:
January 1, 2000
Revised:
December 1, 2001
Online:
January 6, 2003
Citation
Deshpande, M., and Mote, , C. D., Jr. (January 6, 2003). "In-Plane Vibrations of a Thin Rotating Disk ." ASME. J. Vib. Acoust. January 2003; 125(1): 68–72. https://doi.org/10.1115/1.1522419
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