Severe vibrations of the marine propulsion shaft can evidently affect the dynamical response of the propulsion system and degrade the performance of a ship. As the vibration forms couples which interact with each other, a better understanding of the coupled vibrations is essential for dynamic prediction to improve the efficiency and reliability of the marine propulsion system. Thus, an investigation of the lumped-mass method for coupled torsional-longitudinal vibrations of the shaft is proposed. First, a theoretical solution for the coupled ordinary differential equations demonstrates the accuracy of the proposed lumped-mass model. This model allows for the bifurcation diagram and the Poincare surface, and transient accelerations of the coupled vibrations are numerically calculated. Furthermore, the impact factors including various length-diameter ratios, coupling stiffness coefficients, and damping coefficients are respectively discussed. These impact factors are found to affect the coupled vibrations to different extents through the comparison of the transient accelerations. Finally, an accurate and applicative lumped-mass method for the coupled torsional-longitudinal vibrations of the marine propulsion shaft has been obtained. An optimal design and vibration reduction of the shaft, considering the above-mentioned impact factors, can be achieved.
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