Determination of natural frequencies of clamped non-homogeneous trapezoidal plates

Galerkin's method has been applied to study the free transverse vibration of non-homogeneous clamped trapezoidal plates. The assumed deflection function is exactly satisfying the associated boundary conditions. The non-homogenity considered here is a sort of thickness variation. Three different cases, which are, the linear, the exponential and the parabolic thickness variations are considered. The present results for non-homogeneous clamped trapezoidal plates are entirely new and not available elsewhere. Comparisons can only be made for the special cases of non-homogeneous rectangular and homogeneous trapezoidal plates. In these special cases, the results are found to be in good agreement with those previously published in the available literature. A series of tabulated results, for each case of thickness variation is then presented.