Coupled Vibration of Cracked Shafts

The coupling of vibration modes of vibration of a clamped-free circular cross-section Timoshenko beam with a transverse crack is investigated in this paper. A 6 × 6 local flexibility matrix is used to simulate the crack. The nondiagonal terms of this matrix cause coupling between the longitudinal, torsional, and bending vibrations. Coupling is apparent in all spectra obtained with a harmonic sweeping excitation throughout the frequency range. The method is very sensitive even for small cracks.