Objectives  Aiming at the vibration control problem, this paper puts forward a design approach involving longitudinal two-stage vibration isolation technology for ship propeller-shaft systems.

  Methods  First, a mathematic vibration model of a ship propeller-shaft longitudinal two-stage vibration isolation system is established. The effects of design parameters such as mass ratio, stiffness ratio and damping ratio on the vibration characteristics of the system are analyzed. The design is then optimized by using a ship propeller-shaft system as an example.

  Results  The results show that, for a ship propeller-shaft longitudinal two-stage vibration isolation system, the lowest natural frequency ratio control can be obtained according to the formula given in this paper under the given mass ratio or stiffness ratio. With the increase in damping ratio \xi _1 , the attenuation of the vibration transmissibility at the second order natural frequency is more obvious. The optimized ship propeller-shaft longitudinal two-stage vibration isolation system has a better isolation effect than the single-stage vibration isolation system.

  Conclusions  The results of this study have important reference value for the design of ship propeller-shaft longitudinal vibration isolation technology.