Forced vibrations of a marine propulsion shafting with geometrical nonlinearity (primary and internal resonances)

In this paper, the longitudinal primary resonance of a marine propulsion shafting is investigated with special consideration to the case with an internal resonance (the first longitudinal natural frequency is approximately equal to the sum of the first transverse forward and backward frequencies). Coupled longitudinal-transverse dynamic equations of a marine propulsion shafting are established by the Ritz method and the Lagrange equation. Then these equations are solved by the method of multiple scales. The steady-state response and the stability are analyzed. Research shows that the first transverse forward and backward modes could be excited if the longitudinal excitation load is larger than a critical load. There is saturation phenomenon in the longitudinal motion and the extra energy is transferred to the transverse mode. The energy distribution ratio between the forward and backward modes is inversely proportional to their frequency ratio. At last, the effects of damping ratio and frequency detuning parameters on the critical load are discussed. Results of perturbation method are validated by numerical simulations.