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BRIEF NOTES

Multiple Equilibria of a Hydrodynamically Coupled Flexible Disk Rotating Inside a Thin Housing

[+] 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 70(1), 142-147 (Jan 23, 2003) (6 pages) doi:10.1115/1.1526121 History: Received December 16, 2001; Revised July 26, 2002; Online January 23, 2003
Copyright © 2003 by ASME
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References

Iwan,  W. D., and Moeller,  T. L., 1976, “The Stability of a Spinning Elastic Disk With a Transverse Load System,” ASME J. Appl. Mech., 43, pp. 485–490.
Benson,  R. C., and Bogy,  D. B., 1978, “Deflection of a Very Flexible Spinning Disk Due to a Stationary Transverse Load,” ASME J. Appl. Mech., 45, pp. 636–642.
Renshaw,  A. A., 1998, “Critical Speed for Floppy Disks,” ASME J. Appl. Mech., 65, pp. 116–120.
D’Angelo,  C., and Mote,  C. D., 1993, “Aerodynamically Excited Vibration and Flutter of a Thin Disk Rotating at Supercritical Speed,” J. Sound Vib., 168(1), pp. 15–30.
McAllister,  J. S., 1996, “The Effect of Platter Resonances on Track Misregistration in Disk Drives,” Sound Vib., 30(1), pp. 24–28.
Benson,  R. C., 1983, “Observations on the Steady-State Solution of an Extremely Flexible Spinning Disk With a Transverse Load,” ASME J. Appl. Mech., 50, pp. 525–530.
Pelech,  I., and Shapiro,  A. H., 1964, “Flexible Disk Rotating on a Gas Film Next to a Wall,” ASME J. Appl. Mech., 31, pp. 577–584.
Hosaka,  H., and Crandall,  S., 1992, “Self-Excited Vibrations of a Flexible Disk Rotating on an Air Film Above a Flat Surface,” Acta Mech., 3, pp. 115–127.
Chonan,  S., Jiang,  Z. W., and Shyu,  Y. J., 1992, “Stability Analysis of a 2 Floppy Disk Drive System and the Optimum Design of the Disk Stabilizer,” ASME J. Vibr. Acoust., 114, pp. 283–286.
Huang,  F. Y., and Mote,  C. D., 1995, “On the Instability Mechanisms of a Disk Rotating Close to a Rigid Surface,” ASME J. Appl. Mech., 62, pp. 764–771.
Sokolnikoff, I. S., 1983, Mathematical Theory of Elasticity, R. E. Krieger and Co., Malabar, FL.
Bender, C. M., and Orszag, S. A., 1978. Advanced Mathematical Methods for Scientists and Engineers, Springer-Verlag, New York.

Figures

Grahic Jump Location
Displacement versus rotation speed for two disks. (a): A typical Zip disk response without the jump phenomenon; (b): the jump phenomenon at approximately 4500 rpm.
Grahic Jump Location
Schematic of the rotating disk enclosed in a housing
Grahic Jump Location
Contour plot of the number of equilibria as functions of qL and qU.κ=0.291;ν=0.3;Γ=0.114;cL=cU=0.5. The number of equilibria in each region is superimposed on the plot except for the lower left quadrant.
Grahic Jump Location
w(1) versus w(κ) for different qL assuming qU=−qL. Roots indicate equilibrium solutions. κ=0.291;ν=0.3;Γ=0.114;cL=cU=0.5.

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