The marine propulsion shaft is the medium in the marine power transmission system which usually consists of transmission shaft, bearings and other accessories. The multi-stepped beam model is often used for the vibration research of the propulsion shaft. Bearings are considered as the elastic support with certain stiffness value which contains of intermediate bearing, stern bearing etc. In this paper, a general continuous model is presented for the study of the transverse vibration of a real propulsion shaft system under various boundary conditions and the intermediate and stern bearing is considered as the partially elastic support with certain length and location. Energy principle in combination with Rayleigh-Ritz procedure is applied to formulate the problem, in which the displacement is constructed using boundary smoothed Fourier series. Several numerical results are presented to validate the reliability of the current model. The effects of the various boundary conditions are considered. The various stiffness value and locations of the bearing are studied to illustrate the influence to the vibration for the propulsion shaft system. This work can provide an efficient tool for the design and vibration prediction for propulsion shaft system.
