Vibrations of Completely Free Shallow Shells of Curvilinear Planform

[+] Author and Article Information
Y. Narita

Department of Mechanical Engineering, Hokkaido Institute of Technology, Sapporo, Japan

A. Leissa

Department of Engineering Mechanics, Ohio State University, Columbus, Ohio

J. Appl. Mech 53(3), 647-651 (Sep 01, 1986) (5 pages) doi:10.1115/1.3171825 History: Received November 01, 1985; Online July 21, 2009


A method is presented for the free vibration analysis of shallow shells having free edges of arbitrary curvilinear shape. The method of Ritz which was developed for free rectangular plates is extended to the present problem. Components of displacement are expressed as algebraic polynomials. Shells of arbitrary curvature may be treated. Results are obtained for the previously unsolved vibration problems of cylindrical, spherical and hyperbolic paraboloidal shells having free edges of circular and elliptical planform. Convergence of the method is demonstrated. Comparisons with previous solutions are made in the case of zero curvature (i.e., a flat plate). Effects of increasing curvature and ellipticity upon vibration frequencies are examined.

Copyright © 1986 by ASME
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