Finite Element Analysis of Coupled Lateral and Torsional Vibrations of a Rotor With Multiple Cracks

The coupling between lateral and torsional vibrations has been investigated fora rotor dynamic system with breathing crack model. The stiffness matrix has been developed for the shaft element which accounts for the effect of the crack and all six degrees of freedom per node. Since the off-diagonal terms of the stiffness matrix represent the coupling of the respective modes, the special attention has been paid on accurate determination of their values. Based on the concepts of fracture mechanics, the variation of the stiffness matrix over the full shaft revolution is represented by the truncated cosine series where the fitting coefficient matrices are extracted from the stiffness matrices of the cracked shaft for a number of its different angular positions. The variation of the system eigen frequencies and dynamic response of the rotor with two cracks have been studied for various shaft geometries, crack axial locations, and relative phase of cracks. ©2005 ASM