Skip to main content
SpringerLink
Log in

Control of circular-disk stability with membrane stresses

Paper theoretically and experimentally investigates the relationship between the state of disk-membrane stress, critical rotation speed, and the frequency spectrum in radially symmetric disk problems

  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Membrane stresses alter the dynamic behavior and stability of circular-disk elements, such as circular saws and grinding wheels, by shifting the disk's natural frequency spectrum. Such shifts are directly related to variation in the critical rotation speed at which standing-wave-resonance instability occurs. Negative critical-speed variations reduce the disk stability, and positive critical-speed variations increase stability.

The present paper theoretically and experimentally investigates the relationship between the state of disk-membrane stress, critical rotation speed, and the frequency spectrum in radially symmetric disk problems. The observed critical-speed variations are theoretically predictable and well understood. The approach of a shifting critical-speed instability can be predicted by monitoring the disk-frequency spectrum.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

a :

clamping radius

a :

a/b normalized clamping radius

b :

peripheral radius

c :

Initial-stress radius at which the plate is compressed between rollers at gage pressure, P

c :

c/d normalized initial-stress radius

\(\tilde H\) :

1/2 disk thickness

n :

number of nodal diameters

P :

gage pressure applied to initial stressing rollers

ωo :

rotation speed

Ωc :

critical rotation speed

References

  1. Tobias, S. A. andArnold, R. N., “Influence of Dynamical Imperfections on the Vibration of Rotating Disks,”Proc. Inst. Mech. Engrs.,171,669–690 (1957).

    Google Scholar 

  2. Dugdale, D. S., “Stiffness of a Spinning Disc Clamped at Its Centre”,Jnl. Mech. Phys. Solids,14,349–356 (1966).

    Google Scholar 

  3. Mote, C. D., Jr., “Free Vibration of Initially Stressed Circular Disks,”Trans. ASME,87B (2),258–264 (May1965).

    Google Scholar 

  4. Mote, C. D., Jr., “Natural Frequencies in Annuli with Induced Thermal Membrane Stresses,”Trans. ASME,89B (4),611–618 (Nov.1967).

    Google Scholar 

  5. Mote, C. D., Jr., “Stability of Circular Plates Subjected to Moving Loads,”Jnl. of the Franklin Inst., 290 (4),329–344 (Oct.1970).

    MATH  Google Scholar 

  6. Nieh, L. T. and Mote, C. D., Jr., “An Experimental Investigation of the Dynamic Stability of Thin Circular Disks,” Univ. of Calif. Forest Prod. Lab. Report No. 35.01.73 (June 1969).

  7. Mote, C. D., Jr., “Formulation of Discrete Element Models for Stress and Vibration Analysis of Plates,” Univ. of Calif. Forest Prod. Lab. Report No. 35.01.77, (Jan. 1970).

  8. Mote, C. D., Jr., “Unsymmetrical Transient Heat Conduction: Rotating Disk Applications,”Trans. ASME,92B (1),181–190 (Feb.1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of California, 94720, Berkeley, Calif.

    C. D. Mote Jr. (Associate Professor of Mechanical Engineering)

  2. Forest Product Laboratory, University of California, Richmona, Calif.

    L. T. Nieh (Research Assistant)

Authors
  1. C. D. Mote Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. T. Nieh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mote, C.D., Nieh, L.T. Control of circular-disk stability with membrane stresses. Experimental Mechanics 11, 490–498 (1971). https://doi.org/10.1007/BF02327688

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02327688

Keywords

Search

Navigation