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The dynamic behavior of a rotating blade containing a transverse crack was investigated. First, the local flexibility of the cracked blade was obtained by using the method of the released energy. An energy principle, in conjunction with a weighted residual method, was then applied to yield the discrete equations of motion. The equations of motion were further utilized to study the influences of the crack depth and location on the bending natural frequencies under various of rotation speeds. The numerical calculation showed that the crack effects the natural frequencies and the response appreciably only if it is relatively deep and locates near the root of the blade. However, the effects increase exponentially with the depth increases. In addition to the natural frequencies, the displacement responses of the blade with a crack under a constant lateral forces were discussed as well. This was done by calculating the deflections at the tip of the blade for various crack depths and locations. Similar to the rotation speed of the blade frequency, the deflection was offset by the increase of the rotation. However, the centrifugal effects increased significantly such that the crack’s effects became relatively insignificant. Nevertheless, the study showed that the changes on the natural frequency and the tip-deflection of the blade due to a crack may be used as indices for on-line detection of cracks.

Dynamic response and stability of a rotating shaft-disk containing a transverse crack is investigated. FFT analysis of response amplitudes showed that the 2Ω component (Ω: rotation speed) was excited by crack breathing and could serve as a good index for crack identification. Intensive numerical studies of crack location, crack depth, rotation speed, and sensing position on response amplitudes displayed a feasible technique for the identification of crack depth and crack location. It is achieved by intersecting the two equi-amplitude response curves of two separated sensing probes. Finally, the instability of the system caused by a crack is examined via Floquet theory and the multiple scale method. The stability diagrams, illustrated as functions of crack depth, rotation speed, and damping, are shown and discussed.

The dynamic behavior of a rotating shaft-disk-blades system containing a cracked blade is investigated. With the crack released energy, the flexibility due to crack is evaluated. An energy principle in conjunction with the assumed-mode method is applied to yield the discrete equations of motion. Numerical examples are given for cases with between two and five symmetrically arrayed blades. The results show that there exist both torsion-bending coupled modes and blade-coupling modes, which occur at repeated frequencies. When there is a cracked blade, the frequencies of torsion-bending coupled modes decrease due to the crack, and blade-coupling modes have the phenomena of frequency bifurcation. Finally, the effects of shaft speed on the natural frequencies are illustrated.

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