Investigation on an approximation method for solving rectangular cantilever plates including correlation with experiment
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1University of Maryland at BC
2Amirkabir University
3Duke University
In the present study, the vibration problem of rectangular cantilever plates with varying aspect ratio has been investigated by using the classical plate theories based on the Kirchhoff hypothesis. Rayleigh-Ritz method has been adopted for discretization of the problem and using Lagrange equations, the mass and the stiffness matrices have been derived. Using different numbers of structural mode shapes, the convergence of the results has been shown. The theoretical results have been evaluated by using the experimental data obtained from ground vibration experiment carried out at Duke University. It has been shown that for a relatively low aspect ratio rectangular cantilever plate, by using some techniques in Rayleigh–Ritz method lead to an improvement of the results for the natural frequencies. This technique end up having two sets of decoupled equations obtained from the classical plate theory and consequently, the number of equations which have to be solved simultaneously is divided by two. This could lead to a reduction of computational time significantly.
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