Flexural vibrations of axially functionally graded cracked Euler‒Bernoulli beam rotating around a hub

In this thesis, flexural vibrations of axially functionally graded, tapered and cracked beams rotating around a hub are inspected under the different boundary conditions. Rotating beam is modelled in accordance with the Euler‒Bernoulli thin beam theory and rotation based centrifugal effect is taken into account. Material property varying along the beam axis is described by a continuous function. Effects of an open crack occurs on beam are formulated by means of fracture mechanics laws and distributed flexibility model. Energy equations are stated for considered beam conditions and natural frequencies are obtained by the Rayleigh−Ritz method applied using these equations. Effects of taper ratio, hub radius, rotating speed, functional grading factor and crack parameters on non-dimensional natural frequencies are observed and interpreted as a result of the analyses. Results are in good agreement with the results obtained using various methods in literature. Novel results obtained by flexural vibration analyses of axially functionally graded and cracked rotating beams contribute to current literature.