An Energy-Based Equivalent Linearization Method for Non-Smooth Hydrodynamic Damping in Floating Offshore Wind Turbines

Under the combined action of wind and waves, the hydrodynamic loads on a semi-submersible floating offshore wind turbine (FOWT) typically exhibit nonlinear damping characteristics, particularly non-smooth damping at zero velocity. This introduces significant challenges in steady-state response analysis, frequency-domain modeling, and parametric studies. To address this, this paper proposes an energy equivalent linearization method for non-smooth damping based on averaging and energy equivalence principles. Specifically, it equates the nonlinear drag terms in the Morrison equation to a linear damping form that depends on the amplitude, while maintaining the energy dissipation characteristics and amplitude dependence. First, a dynamic model of the semi-submersible FOWT is constructed, and the non-smooth damping form is derived. Next, the equivalent linearization method is introduced and validated under free and forced vibration conditions. Finally, the harmonic balance method is used to analytically solve the equivalent system equations, obtaining the steady-state response of the system. This study attempts to introduce analytical methods into the multi-physics coupled system of FOWT, aiming to provide simple and effective modeling tools for its dynamic analysis, frequency-domain modeling, and engineering applications.