Axisymmetric vibrations and buckling analysis of functionally graded circular plates via differential transform method

• Effect of uniform in-plane force on the axisymmetric vibrations of FGM circular plates is presented.
• Differential transform method has been used to obtain frequency equations for clamped and simply supported plates.
• Frequencies /critical buckling loads for a clamped plate are higher than that for a simply supported plate.
• Mechanical properties of the plate material are assumed to be graded in thickness direction only.
• Two-dimensional mode shapes for the first three frequencies have been plotted.

Analysis and numerical results for the axisymmetric vibrations of functionally graded circular plates subjected to uniform in-plane force have been presented on the basis of classical plate theory. The mechanical properties of the plate material are assumed to vary as a general function of thickness parameter. A semi-analytical approach namely, differential transform method has been employed to solve the differential equation governing the motion of such simply supported and clamped plates. The effect of volume fraction index and the in-plane force parameter has been studied on the first three natural frequencies of vibration. By allowing the frequency to approach zero, the critical buckling loads for both the plates have been computed. Two-dimensional mode shapes for specified plates have been plotted. A comparison of results has been presented.