In this paper, the homotopy analysis method (HAM) is used to give series solutions of self-exited oscillation systems governed by two Van der Pol equations, which are coupled by a linear and a cubic term. The frequency and amplitude of all possible periodic solutions are investigated. It is found that there exist either in-phase or out-of-phase periodic solutions only. Besides, the in-phase periodic oscillations are decoupled, whose periods and amplitudes have nothing to do with the linear and cubic coupled terms. However, the out-of-phase periodic oscillations are strongly coupled, whose period and amplitude can be controlled by the linear and cubic coupled terms.

Floating offshore wind platform (FOWP) has become the economically favored option for supporting wind turbines in deep waters. It is urgent to propose new concept designs for FOWPs that can be effectively deployed. Additionally, the extensive use of steel in such platforms significantly escalates costs, necessitating the optimization of steel utilization. Motivated by these challenges, a V-shaped floating semi-submersible platform equipped with NREL 5 MW wind turbine is designed and analyzed based on the potential flow theory and the blade element momentum theory. Fully coupled time-domain simulations are conducted using the F2A program, which couples NREL FAST and ANSYS AQWA via a Dynamic Link Library (DLL), to compare the hydrodynamic performance and stability of the V-shaped floating platform with the original triangle-shaped model of “Fuyao”. Various sea conditions have been considered, including combined wind-wave action and wind-wave-current action at different incidence angles. The results show that the V-shaped floating platform has better economic and hydrodynamic performance (e.g., a reduction of 40.4% and 12.9%, respectively, in pitch and yaw motions, and a 17.4% reduction in maximum mooring tension), but lower stability than its triangle-shaped counterpart.

A two-dimensional boundary element method (BEM) based on the potential flow theory is adopted to study the combined wave radiation and diffraction by a single barge. The wave-body interaction problems are simulated using a mixed Euler-Lagrangian scheme, with fully nonlinear boundary conditions. The numerical schemes are verified through comparing with existing results, which show that both the wave runups on the barge and hydrodynamic forces can be calculated with sufficient accuracy. Cases of a single barge subjected to sway motion and regular waves are studied. The real contribution of this study is the outcomes of the spectral analysis conducted for test cases when wave radiation effects are considered in addition to pure wave diffraction. The cases of sway motion with the same frequency as incident wave are simulated first. It is found that sway motion will reduce the overall horizontal force when the frequency is lower than a critical frequency. After that, the higher the frequency, the bigger the horizontal force increasing effect. When the frequency of sway motion is lower than that of incident wave, in terms of the magnitude of the horizontal force, sway motion of the body will always make the resultant force larger than that of pure diffraction case.