Flap-wise and chord-wise vibrations of axially functionally graded tapered beams rotating around a hub

This paper presents flap-wise and chord-wise flexural vibration analyses for centrifugally stiffened tapered beams made of functionally graded material in axial direction. Functions of material properties varying along beam are defined in terms of the power law distribution. Calculations are conducted by simple computation technique of the Rayleigh-Ritz method that uses simple shape functions and energy expressions written for centrifugally stiffened Euler-Bernoulli beams. Effects of taper ratio, hub radius, angular velocity and non-homogeneity are inspected for the thin beams with several classical boundary conditions. Results given as non-dimensional natural frequencies are validated by the results given in existing literature and/or the outputs of finite element analyses performed for axially functionally graded solid beam. Achievements and limitations of the method are discussed and clearly reflected.