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01-Applied Mathematics & Information Sciences
An International Journal
               
 
 
 
 
 
 
 
 
 
 
 
 
 

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Volumes > Volume 01 > No. 2

 
   

Generating BCOPs¤ to Compute Natural Frequencies of an Elliptical Plate With Half of the Boundary Simply Supported and the Rest Free

PP: 113-127
Author(s)
Saleh M. Hassan,
Abstract
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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