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In this paper, I presented the analysis and numerical results for freetransverse vibration of thin rectangular plates having arbitrarily varyingnon-homogeneity with the in-plane coordinates along the two concurrent edges.For finding the general governing differential equation first used theKirchhoff's plate theory by considering their assumptions. After finding thegoverning equation for the plate. For the non- homogeneity a linear variationfor Young's modulus and density of the plate has been assumed. Finitedifference method (FDM) has been used to obtain the eigen value problem forsuch model plate for two different boundary condition at the edge namely (i)CCCC fully clamped (ii) CSCS two opposites are clamped and other two are simplysupported. By solving these eigen value problem using MATLAB, the lowest threeeigen value have been reported as the first three natural frequencies for thethree mode of vibration. The effect of various plate parameters such on thevibration characteristics has been analysed. Three dimensional mode shape hasbeen plotted.

Free Transverse Vibration Analysis of thin rectangular plates having arbitrarily varying non-homogeneity along two concurrent edge