Objectives  In order to solve the problem of the longitudinal vibration of submarine propulsion shafting,

  Methods  complex submarine propulsion shafting is simplified to a uniform stepped shaft continuum model, Wave Propagation Analysis (WPA) is used and the longitudinal vibration transfer relationship of each axis is deduced. Combined with the actual propulsion shafting boundary conditions, the steady state response of propeller shaft longitudinal vibration under propeller excitation is obtained.

  Results  The reliability of the model is verified by comparing the theoretical calculated value with the finite element software simulation results and experimental test data, proving that it can be used for the longitudinal vibration analysis of propulsion shafting. Dimensionless formulas for the first natural frequency of the longitudinal vibration of submarine propulsion shafting are deduced, providing convenience for further analysis.

  Conclusions  The results have definite value for engineering applications.