A Method to Simulate the Heave-Pitch Coupled Motion of Spar Platforms

The purpose of this work is to explore the internal resonance exhibited by the heave–pitch coupled motion of a classic Spar platform via an equivalent analog circuit method. First, the pitch motion equation is established on the basis of the motion characteristics of the Spar platform, and a damped Mathieu equation is obtained via normalization. Then, the equivalent analog circuit model of the motion equation is obtained by using operational amplifiers and multipliers as circuit components. The circuit equation is found to be consistent with the motion equation. Finally, the multiparameter equivalent analog circuit model is used to study the coupled motion of a Spar platform. The stable range of the pitch motion of the Spar platform is determined according to threshold conditions. The feasibility of the proposed method is then verified. The results show that the equivalent analog circuit method is effective for obtaining the time history of the pitch motion and predicting the parametric resonance of the Spar platform.