A study on Mathieu-type instability of conventional spar platform in regular waves

In this paper, we consider the vertical motion stability of a spar platform based on a damped Mathieu equation for pitch, which is a coupled effect with heave response. Free-decay tests are performed in a wave tank with a scaled model to determine the natural periods and damping coefficients, and the motions in regular waves are measured. During the experiments, it is observed that pitch motions become unstable when the pitch natural period is double the heave natural period. The underlying mechanism is due to the large heave motion making the GM negative, and consequently the platform motion becomes unstable. In the process, kinetic energy is transferred from heave mode to pitch mode due to nonlinearity. The experimental results are seen to agree well with the numerical analysis. From the stability diagram, it can be seen that the damping plate and strakes significantly reduce the unstable region compared to the spar platform without any damping devices. The damping devices cannot keep the spar platform from a commensurable relation between periods of heave and pitch, but they are capable of stabilizing motion by increasing the damping and restricting heave resonant motion.