Dynamic behavior of Jeffcott rotors with an arbitrary slant crack orientation on the shaft

Dynamic behaviour of a Jeffcott rotor system with a slant crack under arbitrary crack orientations is investigated. Using concepts of fracture mechanics, flexibility matrix and stiffness matrix of the system are calculated. The system equations motion is obtained in four directions, two transversal, one torsional and one longitudinal, and then solved using numerical method. In this paper a symmetric relation for global stiffness matrix is presented and proved; whereas there are some literatures that reported nonsymmetrical form for this matrix. The influence of crack orientations on the flexibility coefficients and the steady-state response of the system are also investigated. The results indicate that some of the flexibility coefficients are greatly varied by increasing the crack angle from 30 ◦ to 90 ◦ (transverse crack). It is also shown that some of the flexibility coefficients take their maximum values at (approximately) 60 ◦ crack orientation