Flap-Wise Vibrations of Axially Functionally Graded and Centrifugally Stiffened Beams with Multiple Masses Having Rotary Inertia

This paper is on flap-wise vibrations of centrifugally stiffened axially functionally graded beams with multiple lumped masses including rotary inertia effects. Material properties are defined along beams' length using the function appropriate to the power law distribution. Energy expressions of Euler-Bernoulli beam model are stated for flexural vibrations of beam with additional multiple masses rotating around a hub. Energy formulations are discretised to apply Rayleigh-Ritz solution method which uses admissible polynomial mode shape function. Analyses are conducted by changing number, size and inertias of additional masses, taper ratios of beam, rotating speed and radius of hub and the power of distribution function of beam material. Non-dimensional parameters are used to reflect results that are validated by those given in current literature. Unique results are also given for the homogeneous and functionally graded beam rotating with multiple masses. Effects of varying parameters and advantages/shortcomings of present solution are reflected and discussed.