Free Vibration and Tension Buckling of Circular Plates With Diametral Point Forces

[+] Author and Article Information
E. F. Ayoub, A. W. Leissa

Department of Engineering Mechanics, Ohio State University, Columbus, OH 43210

J. Appl. Mech 57(4), 995-999 (Dec 01, 1990) (5 pages) doi:10.1115/1.2897673 History: Received June 19, 1989; Revised September 15, 1989; Online March 31, 2008


This paper presents the first known results for the free vibrations of a circular plate subjected to a pair of static, concentrated forces acting on the boundary at opposite ends of a diameter. The closed-form exact solution of the plane elasticity problem is used to provide the in-plane stress distribution for the vibration problem. A proper procedure using the Ritz method is developed for solving the latter problem for clamped, simply supported, or free boundary conditions. Numerical results are given for the vibration frequencies of a simply supported circular plate, which separate into four symmetry classes of mode shapes. Compressive buckling loads for each symmetry class are determined as a special case as the frequencies decrease to zero with increasing compressive force. Tracking the frequency versus loading data with increasing tensile forces shows that buckling due to tensile force can also occur, and the critical value of the force is found.

Copyright © 1990 by The American Society of Mechanical Engineers
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