Free vibration analysis of a rotating single edge cracked axially functionally graded beam for flap-wise and chord-wise modes

Abstract

This study concerns with the free vibration analyses for centrifugally stiffened cracked beams modelled as functionally graded material in the axial direction. The variation of material properties along the cracked beam is expressed in terms of the power law distribution. Analyses are carried out by the Rayleigh-Ritz method that uses shape functions and energy expressions written for centrifugally stiffened Euler-Bernoulli beams. The influence of the hub radius, angular velocity, crack location to beam length ratio and crack depth to thickness ratio and cross-section size ratio and inhomogeneity on natural frequencies are examined for the beams with the clamped-free boundary condition. The results are verified by using the data available in the open literature and/or the outputs of finite element analyses performed for an axially functionally graded solid beam. The results show that the fundamental frequency parameters reduce with the increasing the ratio of crack depth to thickness. The highest natural frequency droop exists close to the root of the beam for flap-wise and chord-wise vibrations. Another important finding is that reduction of natural frequency parameters in chord-wise modes is larger than that in flap-wise modes when the crack location is varied. This new research should help to improve predictions of the impact of the crack on free vibrations for the rotating cracked axially functionally graded beams.