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RESEARCH PAPERS

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

Abstract

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
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