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.
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December 1971
Research Papers
An Asymptotic Solution of a Rotating Disk
C.-H. Wu
C.-H. Wu
Department of Materials Engineering, University of Illinois at Chicago Circle, Chicago, Ill.
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C.-H. Wu
Department of Materials Engineering, University of Illinois at Chicago Circle, Chicago, Ill.
J. Appl. Mech. Dec 1971, 38(4): 971-977 (7 pages)
Published Online: December 1, 1971
Article history
Received:
December 10, 1969
Revised:
October 16, 1970
Online:
July 12, 2010
Citation
Wu, C. (December 1, 1971). "An Asymptotic Solution of a Rotating Disk." ASME. J. Appl. Mech. December 1971; 38(4): 971–977. https://doi.org/10.1115/1.3408984
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