A nonlinear monodimensional beam model for the dynamic analysis of the mast pumping phenomenon in sailing boats

An original mechanical model of the complex hull-mast-sails system is formulated to simulate the essential dynamics of a boat sailing windward. The minimal structural scheme includes a flexible linear cantilever beam, describing the mast, coupled with an inextensible nonlinear cable, representing the foresail supported by the forestay. A rigid body simulates the hull. Considering the periodic pitching motion in the vertical plane, driven by the sea waves, a quasi-static approximation of the wind forces transferred by the cable to the beam tip is adopted. A direct and parametric excitation of the cantilever beam are found to participate in the wind-sail-mast interaction, providing a possiblemechanical interpretation for the onset of high-amplitudemast oscillations. A quadraticallynonlinear one-degree-of-freedom model is obtained through a standard discretization in the reduced base of the fundamental linear mode. Parametric analyses are carried out to assess the importance of the nonlinearities. Finite element analyses confirmand validate the analytical results.