Research On The Large Amplitude Rolling And Stability Of A Ship In Waves

Ship navigation on the sea safety is one of issues that ship designers and user willconcern most. In order to reveal the mechanism of ship capsize, this dissertation use nonlineardynamics methods to analysis the ship nonlinear rolling movement and stability on the seas.The main work and conclusions of this dissertation are as follow:Summarized the nonlinear factors that exist in ship’s large amplitude rolling, analyzedthe methods to calculate the nonlinear terms. Proposed a method that can calculate thenonlinear coefficients of restoring moment of ships rapidly. Established the nonlinear rollingequation of ships on regular beam seas.The multiscale method is used to study the main, ultraharmonic and subharmonicresonances of nonlinear rolling in regular beam seas, and the approximate solutions of thethree resonances were given. At the same time, the characteristics of the threefrequency-amplitude responses were analyzed depending on the secular terms. Thepertubation solutions are compared with solutions obtained by numerical intergration of thenonlinear governing roll equation and the results show that the approximate analysis solutionsare valid.Use different of chaos identification methods to determine the stability of ship in thebeam wave. Analyze and compare the advantages and disadvantages of different methods andindicate bifurcation and chaos will lead to ship capsize. A fast and efficient algorithm forcompute Lyapunov exponents is applied to ship’s nonlinear rolling system. The results showthat this method can judge the state of ship’s nonlinear rolling system accurately.The Melnikov method was used to study the ship’s nonlinear rolling differential equation,a numerical method was presented to compute the melnikov function, and to get the curve ofthreshold above which chaos may occur, the result are validate by safe basin method.In order to increase the stability region of ship in regular beam wave, a feedback controllaw is designed to control the bifurcations taking place in the resonance response, thusremoving or delaying the occurrence of jump and hysteresis phenomena. Numericalsimulations are performed to verify the effectiveness of the proposed feedback control.The stability regions of ship in longitudinal wave are analyzed by the Lyapunov exponents method. A feedback control law is designed to improve the stability of ship inlongitudinal wave, numerical simulations are performed to verify the effectiveness of theproposed feedback control.The combination of the finite difference method and the successive over relaxationmethod is employed to numerically solve the stationary solutions of FPK equation of ship’snonlinear rolling system． The joint probability density function and stationary meanout-crossing rate are investigated for ship nonlinear rolling subjected to additive white noiseexcitation.Basing on the nonlinear dynamics theory, the global stability of ship in stochastic beamsea is researched by the global bifurcation method. Considered the stochastic excitation termas bounded noise and the influence of nonlinear damping and nonlinear righting moment, therandom single degree of freedom nonlinear rolling equation is established. The randomMelnikov mean-square criterion is used to analysis the global stability of this system. Theship’s prarmetrical rolling equation in stochastic longitudinal waves is established, theprincipal resonance of the paramerically excited system is investigated. The method ofmultiple scales was used to determine the equations of modulation of amplitude and phase.The stability and steady state response were studied. The influence of ship’s damping, themain frequences of the stochastic wave and the bandwidth of the waves for the ship’s saftyregin in longitudinal waves are analyzed.