Nonlinear harmonic resonant behaviors and bifurcation in a Two Degree-of-Freedom Duffing oscillator coupled system of Tension Leg Platform type Floating Offshore Wind Turbine

The surge-heave coupled motion model of a Tension Leg Platform type Floating Offshore Wind Turbine (TLP FOWT) is first established. By taking the tendons stretching and platform set-down motion into consideration, the nonlinear model is a Duffing oscillator coupled system. We analyze the nonlinear feature in the surge-heave coupled motions by the semi-analytical algorithms in nonlinear dynamics. The harmonic balance method is applied to obtain the analytical solutions of the nonlinear system under wind and wave excitations. The analytical solution verifies the excellent accuracy. To further achieve the heave motion response, we organize the bifurcation analysis and discuss the effects of the dynamic parameters on the heave responses. The results reveal the multi components of heave motion, which consist of constant, primary harmonic resonate and higher order harmonic resonate. In addition, the change of dynamic parameters has various effects on the response. The increment of wave load leads to the expansion of heave response, and an instantaneous expansion appear. Both linear surge and heave damping only affect the amplitudes of heave motion. The nonlinear surge stiffness and heave stiffness can barely affect the primary harmonic resonance amplitudes, but they present different effects on the higher order harmonic resonance component.