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RESEARCH PAPERS

Deflection of a Very Flexible Spinning Disk Due to a Stationary Transverse Load

[+] Author and Article Information
R. C. Benson

Xerox Corporation, Rochester, N.Y. 14644

D. B. Bogy

Department of Mechanical Engineering, University of California, Berkeley, Calif. 94720

J. Appl. Mech 45(3), 636-642 (Sep 01, 1978) (7 pages) doi:10.1115/1.3424374 History: Received December 01, 1977; Revised May 01, 1978; Online July 12, 2010

Abstract

This paper addresses the problem of steady deflection of a very flexible spinning disk due to transverse loads that are fixed in space. We first approach this problem within the context of membrane theory. The membrane differential operator is classified and shown to be hyperbolic in the outer region and elliptic in the inner portion. The characteristics are studied and qualitatively compared with some experimentally observed standing waves in the outer region of a membrane-like disk. The eigenvalue problem is examined and the membrane operator is found to be singular. We therefore conclude that the problem of interest cannot be solved within the context of membrane theory. Finally, the problem is formulated with bending stiffness retained. The concentrated load problem is solved by use of a Fourier series expansion in the angular direction in conjunction with a numerical solution for the radial modes. Graphical results are presented for various values of the stiffness parameter and load location.

Copyright © 1978 by ASME
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