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BRIEF NOTES

Thickness Profiles for Rotating Circular Disks That Maximize Critical Speed

[+] Author and Article Information
G. M. Warner

A. A. Renshaw

Department of Mechanical Engineering, Columbia University, M/C 4703, New York, NY 10027

J. Appl. Mech 68(3), 505-507 (Dec 05, 2000) (3 pages) doi:10.1115/1.1360182 History: Received March 20, 2000; Revised December 05, 2000
Copyright © 2001 by ASME
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References

Bird, W. M., 1990, “Rotating Saw Blade Having Improved Critical Vibrational Speed,” U.S. Patent Number 4,979,417.
Olhoff,  N., 1970, “Optimal Design of Vibrating Circular Plates,” Int. J. Solids Struct., 6, pp. 139–156.
Thambiratnam,  D. P., and Thevendam,  V., 1988, “Optimum Vibrating Shapes of Beams and Circular Plates,” J. Sound Vib., 121, No. 1, pp. 13–23.
Seireg,  A., and Surana,  K. S., 1970, “Optimum Design of Rotating Disks,” J. Eng. Ind., 92, pp. 1–9.
Berger,  M., and Porat,  I., 1988, “Optimal Design of a Rotating Disk for Kinetic Energy Storage,” ASME J. Appl. Mech., 55, pp. 164–170.
Renshaw,  A. A., 1998, “Critical Speed for Floppy Disks,” ASME J. Appl. Mech., 65, pp. 116–120.
Sokolnikoff, I. S., 1983, Mathematical Theory of Elasticity, R. E. Krieger, Malabar, FL.
Chen,  D.-Y., and Ren,  B.-S., 1998, “Finite Element Analysis of the Lateral Vibration of Thin Annular and Circular Plates With Variable Thickness,” ASME J. Vibr. Acoust., 120, pp. 747–752.
Warner, G. M., and Renshaw, A. A., 1999, “Thickness Profiles for Rotating Circular Disks That Maximize Critical Speed,” 1999 ASME Design Engineering Technical Conference, Las Vegas, NV.
Renshaw,  A. A., 1999, “Increasing the Natural Frequencies of Circular Disks Using Internal Channels,” J. Sound Vib., 229, No. 2, pp. 355–375.
Tadjbakhsh,  I., and Keller,  J. B., 1962, “Strongest Columns and Isoperimetric Inequalities for Eigenvalues,” ASME J. Appl. Mech., 29, pp. 159–164.
Keller,  J. B., and Niordson,  F. I., 1966, “The Tallest Column,” J. Math. Mech., 16, pp. 433–446.

Figures

Grahic Jump Location
Scale drawings of the radial profiles of the saw designs shown in Table 2. (a) Uniform thickness; (b) optimal profile; (c) existing profile. Cross-hatched area represents rigid clamping.

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