0
TECHNICAL PAPERS

Nonlinear Vibration of Rotating Thin Disks

[+] Author and Article Information
Albert C. J. Luo

Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62034-1805

C. D. Mote

Office of the President, Main Administration Building, University of Maryland, College Park, MD 20742

J. Vib. Acoust 122(4), 376-383 (May 01, 2000) (8 pages) doi:10.1115/1.1310363 History: Received February 01, 1999; Revised May 01, 2000
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.

References

Lamb,  H., and Southwell,  R. V., 1921, “The vibrations of a spinning disc,” Proc. R. Soc. London, Ser. A, 99, pp. 272–280.
Southwell,  R. V., 1992, “On the free transverse vibrations of a uniform circular disc clamped at its center, and on the effects of rotation,” Proc. R. Soc. London, Ser. A, 101, pp. 133–153.
Kirchhoff,  G., 1850, “Uber das Gleichgewicht und die Bewegung einer elastischen Scheibe,” J. Reine Angew. Math., 40, pp. 51–88; Kirchhoff,  G., 1850, “Ueber die Schwingungen einer kreisformigen elastischen Scheibe,” Pogg. Ann., 81, pp. 258–264.
Mote,  C. D., 1965, “Free vibration of initially stressed circular plates,” J. Eng. Ind., 87, pp. 258–264.
Iwan,  W. D., and Moeller,  T. L., 1976, “The stability of a spinning elastic disk with a transverse load system,” J. Appl. Mech., 43, pp. 485–490.
von Freudenreich,  J., 1925, “Vibration of steam turbine discs,” Engineering, 199, pp. 2–4 and 31–34.
Campbell,  W., 1924, “The protection of steam-turbine disk wheels from axial vibration,” Trans. ASME, 46, pp. 31–160.
Tobias,  S. A., 1957, “Free undamped nonlinear vibrations of imperfect circular disks,” Proc. Inst. Mech. Eng., 171, pp. 691–701.
Nowinski,  J. L., 1964, “Nonlinear transverse vibrations of a spinning disk,” J. Appl. Mech., 31, pp. 72–78.
Nowinski,  J. L., 1981, “Stability of nonlinear thermoelastic waves in membrane-like spinning disks,” J. Thermal Sci., 4, pp. 1–11.
Advani,  S. H., 1967, “Stationary waves in a thin spinning disk,” Int. J. Mech. Sci., 9, pp. 307–313.
Advani,  S. H., and Bulkeley,  P. Z., 1969, “Nonlinear transverse vibrations and waves in spinning membrane discs,” Int. J. Non-linear Mech., 4, pp. 123–127.
Renshaw,  A. A., and Mote,  C. D., 1995, “A perturbation solution for the flexible rotating disk: Nonlinear equilibrium and stability under transverse loading,” J. Sound Vib., 183, pp. 309–326.
Luo, A. C. J., 1999, “An approximate theory for geometrically-nonlinear thin plates,” Int. J. Solids Struct., in press.
Byrd, P. F., and Friedman, M. D., 1954, Handbook of Elliptic Integrals for Engineers and Physicists, Springer-Verlag, Berlin.

Figures

Grahic Jump Location
Asymmetric, rotating disk with clamped-free boundaries
Grahic Jump Location
Natural frequency of the computer disk predicted through the linear analysis (a=15.5 mm, b=43 mm, h=0.775 mm, ρ0=3641kg/m3,E=69 GPa, ν=0.33)
Grahic Jump Location
Natural frequency (s=0) of the disk. As=f sc2+f ss2 is modal amplitude. Two nonlinear theories give the identical predictions. Two nonlinear models at As=0 reduce to the linear model. (a=15.5 mm, b=43 mm, h=0.775 mm, ρ0=3641kg/m3,E=69 GPa, ν=0.33).
Grahic Jump Location
Natural frequency (s=3) of the hardening disk. As=f sc2+f ss2 is modal amplitude. The solid and dash lines denote this theory and the von Karman theory. Two nonlinear models at As=0 reduce to the linear model. ΩcrLcrK and ΩcrN denote critical speeds predicted through the linear theory, the von Karman theory and the new theory, respectively. (a=15.5 mm, b=43 mm, h=0.775 mm, ρ0=3641kg/m3,E=69 GPa, ν=0.33).
Grahic Jump Location
Natural frequency (s=4) of the hardening disk. As=f sc2+f ss2 is modal amplitude. The solid and dash lines denote this theory and the von Karman theory. Two nonlinear models at As=0 reduce to the linear model. ΩcrLcrK and ΩcrN denote critical speeds predicted through the linear theory, the von Karman theory and the new theory, respectively. (a=15.5 mm, b=43 mm, h=0.775 mm, ρ0=3641kg/m3,E=69 GPa, ν=0.33).
Grahic Jump Location
Natural frequency (s=6) of the softening disk. As=f sc2+f ss2 is modal amplitude. The solid and dash lines denote this theory and the von Karman theory. Two nonlinear models at As=0 reduce to the linear model. ΩcrLcrK and ΩcrN denote critical speeds predicted through the linear theory, the von Karman theory and the new theory, respectively. (a=15.5 mm, b=43 mm, h=0.775 mm, ρ0=3641kg/m3,E=69 GPa, ν=0.33).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In