Finite element dynamic analysis of multibody rotor-bearing system with cracked shaft

The equations of motion of a general multibody system are derived using the Langrangian approach. The multibody system can be an assemblage of flexible as well as rigid bodies. The equations of motion of a rotor-bearing system are deduced from those of the general multibody system. A cracked rotor shaft finite element is developed to model the rotor shaft. The shape functions of the cracked rotor shaft finite element are derived using Timoshenko beam theory and crack flexibility compliance as a parameter. The explicit expressions of the element mass, stiffness and gyroscopic matrices are developed thus obviating the need for extensive numerical computations. A computer scheme is developed to assemble the system equations of motion from the elemental level using finite element assembly procedure. It can invoke either complex or planar modal reduction scheme to reduce the order of the full-order finite element model. The complex modal reduction scheme is implemented for the first time in this dissertation. The reduced order modal equations of motion are integrated forward in time. The mass matrix of the rotor-bearing system is function of time and couples the flexural and torsional vibrations. The numerical scheme updates the mass matrix with time. The vibration characteristics and the transient dynamic response of the cracked rotor-bearing system are studied.