Study On Nonlinear Coupling Dynamic Response Of A Classic Spar Platform

Offshore oil and gas drilling and production activities are being pushed into deeper and deeper waters. As the most attractive types of deep and ultra deep water production platforms, Spars have exhibited excellent dynamic characteristic in normal conditions. But some recent numerical research and experiments results showed that the compliant coupled resonant response appeared when the platform experiencing long periodic ground swell because of some nonlinear factors, which may cause unstable motion and tension increasing quickly in the cable. This phenomenon may endanger the security and production of the platform. More and more attention has been attracted to the motion stability and coupled dynamic response of the Spar platforms in the ocean engineering field presently.In this paper the nonlinear dynamics theory is adopted to study the motion stability of a classic Spar platform and the hull-mooring coupled dynamic response is calculated in regular waves by using the numerical method. The main contents and contribution are summarized as follows:(1) The structure form and general characteristic of the Spar platforms are presented, the development process is reviewed, the application status and the development tendency at abroad are introduced, some recent research achievements of the Spars are summarized synthetically, the study direction and key problems of the thesis are presented.(2) The wave loadings on the hull of a Classic Spar platform are calculated. The coupled differential equations for surge, heave and pitch of a Spar platform are deduced according to the rigid body dynamics theory. The first order wave exciting forces and the radiation damping forces of an experimental Spar model are calculated according to the diffraction/radiation theory, the second order wave exciting force of surge is also obtained which lay a foundation for the further theoretical analysis.(3) The Mathieu instability of pitch motion of a Spar platform is studied. The nonlinear parametric and forcing excited equation for pitch motion is established with considering the effect of heave motion on the metacentric height of pitch. The approximate analytical solution of the differential equation is obtained for the prime parametric by using perturbation method. The stability and the local bifurcation characteristic of the solution are studied according to the Lyapunov's laws so as to reveal the mechanism of instable parametric pitch motion. The parametric field for the large amplitude pitch motion is obtained and the method is founded for predicting the instable pitch movement. The factors of different excited parameters and pitch damping for the response are also analyzed.(4) The internal resonant characteristic of heave-pitch motion is studied. The nonlinear coupling equations for heave and pitch are established considering the effect of time-varying incident wave elevation and first order wave exciting forces. The steady-state response of the equations are solved by the method of multiple scales and validated by the numerical method in the presence of the quasi 2:1 internal relationship when the wave frequency get close to the natural heave frequency. The stabilities steady-state periodic solutions are analyzed according to the Floquet theory. It is observed that the heave motion exhibits saturation when the internal resonance occurs, as the heave exciting force increases further, the extra energy of heave mode is transferred to the pitch mode and induces unstable pitch response. Increasing heave damping can decrease the heave resonant amplitude, Increasing pitch damping or enlarge the disparity of the natural frequencies between heave and pitch motion can weaken the coupled relationship of the two modes, which can suppress the internal resonance response.(5) The combination resonance response of heave-pitch motion is studied. The steady-state response of the equations are obtained when the incident wave frequency approaching to the sum of heave natural frequency and pitch natural frequency. The stabilities and the local bifurcation characteristic of the trivial solution are analyzed according to the Routh-Hurwitz criterion. The result shows that large pitch exciting moment can induce bifurcation behavior in two solution curves and trips stable sub-harmonic component, which leads to period doubling and jumping phenomena in both modes. Increasing system damping can reduce the instability domain of the trivial solution so as to improve the stability of Spar platform.(6) The coupled dynamic response for the hull-mooring system of a Spar platform is calculated under regular waves. The mooring system is modeled by using the lumped masses method, the fluid loads and the coupled effects are taken into account so that a full coupled analysis model of hull/mooring system is established. The large computer program ANCMS is developed adopting Runge-Kutta method with MATLAB. By taken an experimental Spar model for example, the pretension at the fairlead and configuration underwater are obtained with different cable lengths, the mooring stiffness are calculated. The dynamic responses under regular waves with/without mooring lines are compared. The viscous damping and mass inertia effects of the mooring lines on the responses are analyzed, the bifurcation diagram of motion and tension is obtained with the wave frequency as the bifurcation parameter.