This dissertation systematically presented a study on the vibration problem of a specific ship shaft system, including three-dimensional geometry modelling of the whole ship shaft system, the study on the factors that influence on the ship shaft system's intrinsic vibration performance, the vibration response of the ship shaft under different excitation forcing, the study on the cracked shaft's non-linear dynamic performance, the coupled vibration of the ship shaft. The purpose of this dissertation is to gain an insight into the inherent vibration specific characteristic of the ship shafting system. The dissertation is organized as following:Chapter 1 introduced the different vibration of ship shaft system, the cause of the different types of vibration and some research achievement/progress of the ship shaft vibration and some other relative fields. Moreover, this chapter presented the significance, main contents and arrangement of the dissertation.Chapter 2 presented the types of ship shafting vibration, causes of different vibration and the research method; introduced the Finite Element Method (FEM) of the ship shaft system vibration's computation, presented some basic theory of FEM; introduced the software and research method of the research on the topic of this thesis; presented a specific ship's shaft system's parameter, set up a detailed three-dimensional model of the ship shaft.In Chapter 3, based on the FEM software ANSYS, studied the many factors that have some effect on the ship shaft system's inherent vibrational performance, including controllable pitch propeller's effect, the support bearing's influence on the shaft's vibration, the effect of shaft non-alignment, effect of shaft bending and the effect of gear meshing.In Chapter 4, used the Finite Element Method, computed and analyzed the vibration response of the ship shaft system under different excitation forcing, including the shaft's response under propeller's excitation, the shaft's response under gear meshing excitation, shaft's vibration response under ship hull random excitation. As the simulation result, the propeller's excitation has the most influence on the shaft's vibration. So in any research on the ship shaft system's vibration, the propeller's effect muse be considered.In Chapter 5, based on other's model of cracked shaft, used Matlab/Simulink simulation method, studied the factors that have effect on the cracked shaft's non-linear vibration. At the same time, compared the cracked shaft and the specific ship shaft, analyzed the non-linear vibration performance of the ship shaft with crack. Through the numerical simulation, presented some performance of the research object.In Chapter 6, based on some coupled vibration mathematic model, through the numerical simulation, studied some rotor system's lateral-bending coupled vibration and lateral-bending-axial coupled vibration, got some conclusions. Because the ship shaft vibration is lateral-bending-axial coupled vibration under different excitation forcing, so this chapter's research is the base or start point of other research, this chapter also provided the base for continued ship shaft vibration research and other coupled vibration research of other rotors.In the last chapter, the main work, research characteristic and the innovations of this dissertation are briefly concluded. Some unsolved problems and continued work that worth studying are addressed.