Free Vibration Analysis of Rotating Functionally Graded Annular Disc of Variable Thickness Using Generalized Differential Quadrature Method

In this paper, free vibration analysis of rotating annular disc made of functionally graded material (FGM) with variable thickness is presented. Elasticity modulus, density and thickness of the disc are assumed to vary radially according to a power low function. The natural frequencies and critical speeds of the rotating FG annular disc of variable thickness with two types of boundary conditions are obtained employing the numerical generalized differential quadrature method (GDQM). The boundary conditions considered in the analysis is the both edges clamped (C-C) and the inner edge clamped and the outer edge free (C-F).The influence of the graded index, thickness variation, geometric parameters and angular velocity on the dimensionless natural frequencies and critical speeds are demonstrated. It is shown that using a plate with a convergent thickness profile, we have a higher critical speed and natural frequency and using a divergent thickness profile, we can lower the critical speed. It is found that increase in the ratio of inner-outer radii could increase the critical speed of the FG annular disk. The results of the present work could improve the design of the rotating FG annular disk in order to avoid resonance condition