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Generating BCOPs¤ to Compute Natural Frequencies of an Elliptical Plate With Half of the Boundary Simply Supported and the Rest Free |
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PP: 113-127 |
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Author(s) |
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Saleh M. Hassan,
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Abstract |
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| Boundary characteristic orthogonal polynomials in two variables
(BCOPs) have been built up over an elliptical domain occupied by a
thin elastic plate. Half of the plate boundary, y · 0, is taken
simply supported while the other half is kept free. The orthogonal
polynomial sequence (OPS) is generated from a set of linearly
independent functions satisfying the essential boundary conditions
of the problem and tabulated in advance, once and for all, for
various values of the aspect ratio r = b=a of the plate with the
desired precision. Free flexural vibrations of the plate have been
examined by using these polynomials in the Rayleigh-Ritz method.
Successive approximations have been worked out to ensure
convergence. Comparisons have been made with known results in
literature. Three-dimensional mode shapes and the associated contour
lines have been plotted in some selected cases. |
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