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.
Vibration and Post-buckling of In-Plane Loaded Rectangular Plates Using a Multiterm Galerkin’s Method
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, June 27, 2001; final revision, January 29, 2002. Associate Editor: N. C. Perkins. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Ilanko, S. (August 16, 2002). "Vibration and Post-buckling of In-Plane Loaded Rectangular Plates Using a Multiterm Galerkin’s Method ." ASME. J. Appl. Mech. September 2002; 69(5): 589–592. https://doi.org/10.1115/1.1489449
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