  In this paper, I presented the analysis and numerical results for free
transverse vibration of thin rectangular plates having arbitrarily varying
non-homogeneity with the in-plane coordinates along the two concurrent edges.
For finding the general governing differential equation first used the
Kirchhoff's plate theory by considering their assumptions. After finding the
governing equation for the plate. For the non- homogeneity a linear variation
for Young's modulus and density of the plate has been assumed. Finite
difference method (FDM) has been used to obtain the eigen value problem for
such 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 simply
supported. By solving these eigen value problem using MATLAB, the lowest three
eigen value have been reported as the first three natural frequencies for the
three mode of vibration. The effect of various plate parameters such on the
vibration characteristics has been analysed. Three dimensional mode shape has
been plotted.
