A procedure to calculate the natural frequencies of in-plane loaded, thin, slightly curved, simply supported rectangular plates is presented, with numerical results. This includes the solutions to von Karman’s static equilibrium equation and the linear shell vibration equation using Galerkin’s method. The compatibility equations are given in terms of Airy stress functions which satisfy the “shear free” and “constant normal displacement” in-plane edge conditions. This procedure is an extension to the method presented by Hui and Leissa, the difference being the use of a multiterm Fourier series representation for the initial imperfection, the static deflection and the vibratory modes.

Issue Section:
Technical Papers
Keywords:
vibrations, buckling, Galerkin method, stress analysis
Topics:
Buckling, Plates (structures), Stress, Vibration, Displacement, Equilibrium (Physics)
1.
Hui
,
D.
, and
Leissa
,
A. W.
,
1983
, “
Effects of Geometrical Imperfections on Vibrations of Biaxially Compressed Rectangular Flat Plates
,”
ASME J. Appl. Mech.
,
50
, pp.
750
–
756
.
2.
Harrington, J. J., 1993, “The Small Amplitude Vibrations of Geometrically Imperfect, Simply Supported, Rectangular Plates,” BE Project Report No. 28, Department of Mechanical Engineering, University of Canterbury, New Zealand.
Copyright © 2002
 by ASME
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