Free vibration analysis of rotating functionally graded annular disc of variable thickness using generalized di erential 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 Dierential Quadrature Method (GDQM). The boundary conditions considered in the analysis are both edges clamped (C-C): the inner edge clamped and outer edge free (C-F). The in uence of the graded index, thickness variation, geometric parameters, and angular velocity on the dimensionless natural frequencies and critical speeds is demonstrated. It is shown that we have higher critical speed and natural frequency using a plate with a convergent thickness prole, and lower critical speed using a divergent thickness prole. It is found that the 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.