Numerical modeling and experimental analysis on coupled torsional-longitudinal vibrations of a ship's propeller shaft

A simplified lumped-mass model was established using ordinary differential equations, focusing on the coupled torsional-longitudinal vibrations of a ship's propeller shaft. The numerical simulation based on the presented algorithm was then developed and the dynamic behavior was investigated. A theoretical solution setup with simple model was solved to demonstrate the accuracy of the proposed lumped-mass model. Based on this model, the coupled natural frequencies and the maximum acceleration of each direction were determined. Experimental tests were conducted to validate the applicability of the numerical model, over a range of rotational speeds and loading conditions. It is found that the natural frequencies are unaffected while the maximum acceleration are increased with the rotational speed as well as the loading. Natural frequencies representing other directions are induced by the coupling effect, and enhance the dynamical response. The ultimate response in the direction without excitation is enlarged because of the coupling effect. An appropriate coupling stiffness coefficient value has been proposed based on the discussion on modeling and experimental results.