Research On Nonlinear Motion Characteristics Of Surf-riding/Broaching And Surf-riding Probability Of A Ship In Following Waves

The static stability criterion cannot measure the stability of the ship in the wave due to its own limitations.The International Maritime Organization(IMO)is committed to the development of the second generation of complete stability criteria,including surf-riding and broaching,excessive acceleration and loss of pure stability,etc.Based on this background,this paper studies the ship’s instability mode of surfriding and broaching in waves.In this paper,the research of surf-riding and broaching is divided into two stages: the first stage is the conversion of the ship’s periodic motion into the surf-riding state,and the second stage is ship broaching after the instability of surf-riding.The study of first stage is based on the single-degree-of-freedom equation of surge motion.The critical ship speed at which the surf-riding is generated is determined by the Melnikov method and the Runge-Kutta numerical method.Through the phase plan,the transition mechanism of the ship motion from periodic motion to surf-riding is analyzed with the increase of ship speed.Based on the MMG theory,the four-degree-of-freedom maneuverability equations of the surge-sway-yaw-roll motion are established,and the rudder automatic control equation is added.The motion response obtained by numerical method is compared with the model experiments,and the influence of initial position and righting arm on ship motion response is also studied.Given the initial conditions,the Newton iteration method is used to solve the equilibrium points of surf-riding motion and their stability is analyzed.The stochastic Melnikov method and Monte Carlo method are used to study the probability of surf-riding in random waves.The random Melnikov method treats the surf-riding motion as the Hamiltonian system under small disturbance,and treats the random wave excitation process as Gaussian random process to solve the surf-riding probability.The numerical method solves the ship surge response in random waves by the fourth-order Runge-Kutta method.The harmonic superposition method is used to generate the random wave rising.By deriving the phase of each simple harmonic,the instantaneous frequency and instantaneous wave number of the ship’s position are obtained,then the instantaneous velocity of wave is obtained.The Monte Carlo method obtains the probability of riding waves in random seas by counting a large number of response samples to verify the correctness of the analytical method.Sensitivity analysis of the probability of a ship surf-riding in random waves is carried out to study the influence of wave parameters(characteristic wave height and characteristic wavelength)and ship navigation parameters(speed and heading angle)on the surf-riding probability.