Coupled longitudinal-transverse dynamics of a marine propulsion shafting under superharmonic resonances

Abstract

In this paper, the transverse superharmonic resonances of a marine propulsion shafting are investigated under the first blade frequency excitation. A coupled longitudinal-transverse dynamic model due to geometrical nonlinearity is established by Hamilton’s principle and then is discretized by Galerkin method. The method of multiple scales is applied to these equations. The steady-state response and the stabilities are analyzed. The effect of the support stiffness, load, mass of propeller, damping ratio and slender ratio on the nonlinear effect is discussed. Research shows smaller values of slender ratio, bigger values of load and smaller values of damping ratio lead to stronger nonlinear effect. The nonlinear effect is reduced by increasing the back stern bearing stiffness and increased by increasing the front stern bearing and thrust bearing stiffness and the propeller mass. While the middle bearing makes small influence to it. It is also shown that these resonance curves are of the hardening type. Results of perturbation method are agreement with numerical simulations.