A Study on the Combination Resonance Response of a Classic Spar Platform

The sum type combination resonance response of a classic spar platform is studied under a long periodic regular wave in this paper. The nonlinear differential equations for heave and pitch are established considering the time-varying incident wave elevation which is regarded as a parametric excitation. The first order steady-state response is solved by the method of multiple scales when the incident wave frequency approaches the sum of heave natural frequency and pitch natural frequency. The heave and pitch responses of a practical spar platform are obtained by solving the bifurcation equation using a numerical method. It is observed that the large amplitude sub-harmonic motion of heave and pitch mode are tripped when the wave height exceeds a certain value. The result shows that the spar platform may exhibit complicated dynamic behaviors when the sum type combination resonance occurs and indicates that the available damping plays a very important role in suppressing the instable motion responses.