Study On The Nonlinear Motion Characteristics Of Ship In Longitudinal And Oblique Seas

Sailing ships must be adjusted to longitudinal or oblique sea condition when encounter severe sea state, for the sake of avoid wave and wind loads acting on large area; and the ultimate stable state of mooring ship and compliant marine structure in wave is oscillation in longitudinal wave position. But large rolling and capsizing of ship sailing in longitudinal and oblique waves can be seen both in experiments and real navigations; and many different oscillation forms of mooring ship and compliant marine structure exist, some of which may lead to structural failure and cable broken.This paper aims at studying the parametrically excited ship rolling in longitudinal and oblique sea states, discussing dynamic characteristics of mooring ship and dynamic tension of mooring cable in longitudinal wave position. Main contents and conclusions obtained in this paper are as follows:The method for the calculation of metacentric height fluctuation is derived for ship sailing in longitudinal and oblique seas, considering the impact of wave profile and assuming quasi-static equilibrium of heave and pitch motions. The parametrically excited and forcedly-parametrically excited equations of ship rolling in longitudinal and oblique seas are established.The approximate analytical solutions are obtained for the primary parametric resonance of ship rolling in regular longitudinal and oblique seas, by using multiple scales method. The bifurcation surface is obtained by using perturbation method and Floquet theory,in different parametric excitation amplitudes and forcedly excitation amplitudes. The real navigation condition for primary parametric rolling and capsizing is found. Probability density function of random roll amplitudes is derived in random longitudinal sea state, by using stochastic averaging method and FPK equation. Ship rolling time histories in regular and random seas are gained by using numerical simulation method.Numerical simulations and analytical results show: in longitudinal and oblique seas, ship may be subjected to primary parametric resonance with large roll amplitude and even capsizing, when encounter frequency is near the twice of roll natural frequency, wave length and ship length are of the same order and the wave height is larger than a certain value; in oblique seas, ship roll motion is a forcedly-parametrically excited oscillation, primary resonance occur as the encounter frequency is near the roll natural frequency, which may lead to large rolling and capsizing too. To avoid the occurrence of sea accidents, sailing speed and heading angle may be changed to modify the encounter frequency and excitation amplitudes, in order to keep them away from resonance areas.The two degree freedom analysis model for articulated tower-tanker system is established, considering the piecewise-nonlinear characteristic of cable tension. Wave loads on articulated tower and tanker are calculated by using Morison equation and potential flow theory. The motion and dynamic cable tension of the mooring system are calculated using numerical simulation method. The mooring system in this paper is composed of an articulated tower with 88.4m height, a 100000-tonnage tanker and a mooring cable. The bifurcation diagram of this system is obtained with the frequency ratio as the bifurcation parameter. Influences of different system and environmental parameters are discussed.Numerical simulation results show: sub-harmonic resonance exist in some range of wave frequency, and period-doubling bifurcation is observed; low frequency drift of nonlinear mooring system also exist in regular waves, and the cable tension corresponded to this motion is larger than other motion; the range of wave frequency corresponding to low frequency drift will increase when increase the wave force amplitude or reduce the system damping; as wind and current force increases, the range of wave frequency corresponding to subharmonic resonance and low frequency drift motion will move to the direction of higher frequency and disappear gradually.