On the parametric excitation of vertical elastic slender structures and the effect of damping in marine applications

The dynamic behaviour of vertical slender structures for marine applications under parametric excitation is considered. The governing equations are treated using two different numerical schemes. The effect of parametric excitation is examined in cases where the excitation frequency lies in the vicinity of nonlinear resonances. First, the un-damped case is considered and the features of the dynamic response are properly identified and discussed. For explaining the particulars of the un-damped behaviour, the governing equations are treated analytically by applying the method of normal forms. The effect of damping is examined through comparative numerical computations of the system's behaviour. It is shown that the inclusion of hydrodynamic drag in the describing model eliminates the impacts of internal resonances excited due to the parametrically imposed motions. Finally, the paper demonstrates the significance of the terms that describe the coupling between the longitudinal and transverse vibrations.