Vibrations of nonhomogeneous orthotropic rectangular plates with bilinear thickness variation resting on Winkler foundation |
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Authors: | Yajuvindra Kumar R Lal |
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Institution: | 1.Department of Mathematics,Indian Institute of Technology Roorkee,Roorkee,India |
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Abstract: | Free transverse vibrations of nonhomogeneous orthotropic rectangular plates with bilinear thickness variation resting on Winkler
foundation are presented here using two dimensional boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method
on the basis of classical plate theory. Gram-Schmidt process has been used to generate orthogonal polynomials. The nonhomogeneity
of the plate is assumed to arise due to linear variations in elastic properties and density of the plate material with the
in-plane coordinates. The two dimensional thickness variation is taken as the Cartesian product of linear variations along
the two concurrent edges of the plate. Effect of nonhomogeneity parameters, aspect ratio and thickness variation together
with foundation parameter on the natural frequencies has been illustrated for the first three modes of vibration for four
different combinations of clamped, simply supported and free edges correct to four decimal places. Three dimensional mode
shapes for specified plate for all the four boundary conditions have been plotted. A comparison of results in special cases
with published one has been presented. |
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