Research On Nonlinear Dynamics Characteristics Of Ship’s Surf-Riding,Broaching And Pure Loss Of Stability

In the second generation stability rules issued by the International Maritime Organization(IMO),five instability modes of ships are proposed.In this paper,two instability modes of the second generation integrated stability code are studied: surfriding / broaching and pure loss of stability.The analysis of the shipwreck shows that surf-riding / broaching and pure loss of stability are the important reasons for the capsizing or large-scale motion of the ship.In this paper,the nonlinear dynamic method is combined with the method of ship dynamics to study the nonlinear dynamic characteristics of the two ship instability modes,analyze the conditions of the two instability modes,and reveal the mechanism of ship motion instability,which is of great theoretical significance and engineering significance.In the study process of surf-riding,the ship’s surge motion equation under longitudinal wave condition will be established to describe wave riding.Taking ITTC A2 fishing vessel as an example,the surge motion equation will be solved by Malenkov method and Runge-Kutta method respectively.The critical value of riding wave will also be obtained.Threshold maps of Malenkov function will be given,and then the relationship between critical speed and wave is obtained.In the numerical calculation,the time-history curves and phase diagrams of the ship’s wave surf-riding and non-surfriding will be provided respectively,and their non-linear characteristics will be analyzed.The bifurcation diagrams of the ship’s surf-riding motion will be drawn with the speed of the propeller as the bifurcation parameter.Finally,the instability conditions of the ship’s surf-riding can be obtained.As for the broaching motion mode,the response maneuverability formula will be used to establish the yaw motion equation describing the broaching motion.The approximate analytical solution and stability region will be obtained by using the multi-scale method.And then the ship motion characteristics will be numerically calculated under the conditions of 2 and 1.5 times frequencies.The bifurcation diagram of ship’s yaw motion varying with wave height will be drawn.Finally,the critical condition of ship’s broaching instability will be given.In the mode of pure loss of stability,the rolling motion equation describing the pure loss of stability will be established.The restoring arm function of the ship in waves will be calculated by numerical method and be fitted into the equation as a polynomial.The solution of the rolling equation will be calculated with Runge-Kutta method under the condition of 1.5 times and 1 time of the captain’s wavelength respectively.Then the time history curve of the motion and the phase diagram characteristics of the ship’s rolling motion will be analyzed.The bifurcation diagram of ship rolling motion varying with speed will be drawn.Finally,the range of ship speed where loss of pure stability occurs will be provided.In this paper,based on the method of nonlinear dynamics,the conditions of ship’s surf-riding / broaching and pure loss of stability are studied,the bifurcation characteristics of surf-riding / broaching and pure loss of stability are obtained,the critical parameters of ship’s surf-riding / broaching is given,and the speed range of pure loss of stability under certain marine environment is proposed.In this paper,the nonlinear dynamic characteristics of two instability modes proposed by IMO are studied comprehensively.It has reference value for the further improvement and revision of the second generation stability specification.