STUDY ON THE PARAMETRICALLY EXCITED MATHIEU INSTABILITY OF A CLASSIC SPAR PLATFORM

The parametrically excited differential equation for the pitch motion of a classic Spar platform is established considering the effect of time-varying metacentric height value. Then it is simplified to a cubic nonlinear Mathieu equation. The second order steady-state response of the differential equation is solved by the method of multiple scales when the heave frequency is approximately twice as larege as the pitch natural frequency. The stabilities of trivial solution and steady-state periodic solution are analyzed according to the Floquet theory and verified by the numerical method. The result shows that the value plays a very important role in the stability of pitch movement. Adjusting value or increasing system damping can reduce the unstable region of steady-state solution so as to suppress parametrically excited pitch motion.