Modal characteristics of cracked rotors using a conical shaft finite element

A finite element model of a tapered rotating cracked shaft is developed for modal analysis and dynamic modeling of rotor-bearing systems. The finite shaft element has ten degrees of freedom and accounts for linear tapering. The flexibility compliance due to the crack is computed using fracture mechanics approach. The formulation of the tapered rotating cracked finite element includes shear deformation and rotary inertia. The shape functions are derived and explicit expressions for the element mass, stiffness and gyroscopic matrices are obtained using consistent mass formulation. The generalized eigenvalue problem is defined and numerical solutions are obtained for a wide range of whirl ratios, crack depths and crack locations. Comparisons with other results reported in the literature are presented.