Objectives  Due to the larger length-to-diameter ratio of the stern bearing, it is difficult to reflect its actual operating conditions when simplified to the traditional equivalent model of single-point support. Therefore, the influence of the equivalent form of the stern bearing on the transverse vibration characteristics of the shafting is investigated.

  Methods  The improved Fourier series is introduced to describe the lateral vibration displacement of propulsion shafting. Then, the calculation model of lateral vibration performance of propulsion shafting under various equivalent forms, such as single-point support, multi-point support or continuous distributed support, are constructed based on the energy principle. Thereby, the influence of the change of support stiffness equivalent to the liquid film pressure on the lateral vibration of the shafting and the influence of the propeller excitation on the vibration response of the shafting are further analyzed. Finally, the results acquired by the proposed model is compared with the results of related references and finite element method (FEM) to verify the validity of the calculation model.

  Results  The multi-point support calculation results converge to the continuous distributed support calculation results. The three-point support equivalent form can be used to study the influence of liquid film pressure distribution on the lateral vibration characteristics of the propulsion shafting. The shafting response under propeller excitation is affected by the revolution speed.

  Conclusions   The research indicates that three-point support equivalent form can be used to analyze the influence of liquid film pressure on the shafting lateral vibration performance. The proposed model in this paper has advantages of good convergence, high accuracy, and less cost-consuming.