This study pertains to analysing the dynamical behaviour of a floating body undergoing
parametric resonances. A simple vertical cylinder, representing a classical spar-buoy,
is considered, limiting its motion to heave and pitch degrees of freedom. Its geometry
and mass distribution are chosen such that a 2:1 ratio of heave to pitch/roll natural
frequency makes the spar-buoy prone to parametric resonance. The system is then studied
by the shooting method, combined with a pseudo-arclength continuation, and the harmonic
balance procedure. Results show that an extensive bistable region exists, where stable
parametric resonance coexists with a regular resonance response. The analysis also
unveiled the existence of stable quasiperiodic motions existing in correspondence
of both pitch and heave resonance. Results are qualitatively validated using a model
based on the explicit nonlinear Froude–Krylov force calculation.
