An Asymptotic Solution of a Rotating Disk

[+] Author and Article Information
C.-H. Wu

Department of Materials Engineering, University of Illinois at Chicago Circle, Chicago, Ill.

J. Appl. Mech 38(4), 971-977 (Dec 01, 1971) (7 pages) doi:10.1115/1.3408984 History: Received December 10, 1969; Revised October 16, 1970; Online July 12, 2010


The solution of the problem of a thin circular disk rotating at a constant angular velocity about its axis is obtained as a formal power series of the thickness-diameter ratio. The matching of the inner and outer expansions at a circular edge is carried out in detail for the stress conditions as well as for the displacement conditions. While the matching procedure at a stress boundary is well known, the matching procedure at a displacement boundary does not seem to have been treated thoroughly before. We accomplish the matching at a displacement boundary systematically by invoking Betti’s reciprocal theorem. The method is essentially that used by Shield in determining the resultant force on a displacement boundary. The procedure can be generalized to obtain the matching conditions at a mixed boundary.

Copyright © 1971 by ASME
Your Session has timed out. Please sign back in to continue.





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