We present a study of the nonlinear coupling internal resonance for the heave roll and pitch performance of a spar platform under the wave and vortex-induced loads when the ratio of the frequencies of heave, roll and pitch are approximately 2:1:1. In consideration of varying wet surface, the three DOFs nonlinear coupled equations are established for the spar platform under the effect of the first-order wave loads in the heave and pitch, and vortexinduced loads in the roll. By utilizing the method of multi-scales when the vortex-induced frequency is close to the natural roll frequency, the first-order perturbation solution is obtained analytically and further validated by the numerical integration. Sensitivity analysis is performed to understand the influence of the damping and the internal detuning parameter. Two cases with internal resonance are shown. The first case is that no saturation phenomenon exists under small vortex-induced loads. The first order perturbation solution illustrates that only the vortex-induced frequency motion in roll and the super-harmonic frequency motion in heave are excited. The second case is that the vortex-induced loads are large enough to excite the pitch and a saturation phenomenon in the heave mode follows.The results show that there is no steady response occurrence for some cases. For these cases chaos occurs and large amplitudes response can be induced by the vortex-induced excitation.
This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.
The dynamic analysis of a Tension Leg Platform(TLP) in random wave is investigated by considering the set-down of a floating body.The nonlinear restoring stiffness is derived with the set-down motion of a floating body and the coupled motion of the tension leg and platform and the differential equations of the motion are established.The study focuses on the influence of the set-down motion on the nonlinear response of the platform.By considering different significant wave heights and currents,motion responses of the platform are calculated and compared.The analysis shows that the set-down motion significantly increases the heave motion with low frequency and the equilibrium position of the heave motion with the set-down motion is much lower than that without set-down motion.The results in this paper indicate that the set-down motion has a major impact on the safety of the platform inproduction operation,and it is also a threat to the strength of tension legs and risers.
Parametric instability of a riser is caused by fluctuation of its tension in time due to the heave motion of floating platform. Many studies have tackled the problem of parametric instability of a riser with constant tension. However, tension in the riser actually varies linearly from the top to the bottom due to the effect of gravity. This paper presents the parametric instability analysis of deepwater top-tensioned risers(TTR) considering the linearly varying tension along the length. Firstly, the governing equation of transverse motion of TTR under parametric excitation is established. This equation is reduced to a system of ordinary differential equations by using the Galerkin method. Then the parametric instability of TTR for three calculation models are investigated by applying the Floquet theory. The results show that the natural frequencies of TTR with variable tension are evidently reduced, the parametric instability zones are significantly increased and the maximum allowable amplitude of platform heave is much smaller under the same damping; The nodes and antinodes of mode shape are no longer uniformly distributed along the axial direction and the amplitude also changes with depth, which leads to coupling between the modes. The combination resonance phenomenon occurs as a result of mode coupling, which causes more serious damage.
Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model.In fact,in addition to the heave and pitch which are in one plane,the nonlinear unstable motion will also occur in roll.From the results of the experiments,the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch.The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force.The nonlinear coupled equations in heave,roll and pitch are established by considering time-varying wet surface and coupling.The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency.Numerical integration of the motion equations has been performed to verify the first-order perturbation solution.The results are confirmed by model test.There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch.It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value.The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch.The energy transfers from heave to pitch and then transfers from pitch to roll.Due to the influence of the low-frequency vortex-excited force,the response of roll is more complicated than that of pitch.
