NONLINEAR ROLLING STABILITY AND CHAOS RESEARCH OF TRIMARAN VESSEL WITH VARIABLE LAY-OUTS IN REGULAR AND IRREGULAR WAVES UNDER WIND LOAD

The trimaran vessel rolls strongly at low forward speed and may capsize in high sea conditions due to chaos and loss of stability, which is not usually considered in conventional limit-based criteria. In order to perfect the method of measuring roll performance of trimaran, a set of nonlinear roll motion stability analysis method based on Lyapunov and Melnikov theory was established. The nonlinear roll motion equation was constructed by CFD and high-order polynomial fitting method. The wave force threshold of rolling chaos in regular waves is calculated by Gauss-Legendre numerical integration method. The limited significant wave height of rolling chaos in random sea conditions is deduced by the phase space transfer rate, and the complex effect of wind load is superposed in the calculation. The influence of trimaran configuration on the roll system is analyzed through the state differentiation of homoclinic and heteroclinic orbit in phase portrait. The calculation of the maximum Lyapunov exponent further verified the applicability of Melnikov method, and the topological structure change of gradual failure of the rolling system is analyzed by the erosion of safe basin. The complex changes of the nonlinear damping coefficient and the nonlinear restoring moment coefficient caused by the change of the transverse lay-outs between the main hull and side hull have a significant influence on chaos and stability, and the existence of wind load has a certain weakening effect on the stability and symmetry of the system. The conclusion also further indicates the importance of the lay-outs to the dynamic stability of the trimaran vessel, which is significant for its seakeeping design.

Stability and Chaos Analysis of Nonlinear Roll Motion of Trimaran Ship With Variable Lay-Out Under Wind and Waves

The combined action of wind and waves has a great influence on the dynamic stability of roll motion of a trimaran ship, which may get into chaotic situation even capsizing. The lay-out of the trimaran is the main factor influencing the roll performance and its dynamic stability. In order to study the stability performance of the roll motion, firstly, the nonlinear roll motion equations under transverse wind and beam waves are established, in which the main coefficients are obtained by CFD method combined with model test. Then, the Hamilton system is used to analyze the phase portraits of the homoclinic and heteroclinic orbits under different transverse spacing. Finally, the Melnikov function is used to calculate the critical wave threshold of the asymmetric system under the combined action of wind load and wave force, and the Lyapunov exponent based on RHR algorithm was used to verify it. A series of significant conclusions are obtained by comparing the calculation models of different transverse spacing, which can provide references for the design of the trimaran ship.

Long-Term Extreme Response and Reliability of a Vessel Rolling in Random Beam Seas

In this paper, the long-term extreme response of a vessel rolling in random beam seas and the associated reliability evaluation are addressed. The long-term response analysis is based on the upcrossing rates of the roll motion under different sea states. Generally, for nonlinear roll motion in random seas, the high-level roll response is sensitive and closely related to the nonlinear effects associated with the restoring and damping terms. Therefore, assessing the corresponding statistics of the random roll motion with low probability levels is difficult and time-consuming. In this work, the Markov theory is introduced in order to tackle this problem. Specifically, for the dead ship condition, the random roll excitation moment is approximated as a filtered white noise process by applying a second-order linear filter and an efficient four-dimensional (4D) path integration (PI) technique is applied in order to calculate the response statistics. Furthermore, the reliability evaluation is based on the well-known Poisson estimate as well as on the upcrossing rate calculated by the 4D PI method. The long-term analysis and reliability evaluation of the nonlinear roll motion in random seas, which consider the variation of the sea states could be a valuable reference for ship stability research.

Long-Term Extreme Response of a Vessel Rolling in Random Seas

In this paper, the long-term extreme response of a vessel rolling in random beam seas is addressed. The long-term response analysis is based on the upcrossing rates of the roll motion under different sea states. However, the nonlinear effects associated with the restoring and damping terms have a significant influence on the high-level response, assessing the corresponding statistics, such as the upcrossing rate, with low probability levels is difficult and time-consuming. In this work, the Markov theory is introduced in order to tackle this problem. Specifically, the random roll excitation moment is approximated as a filtered white noise process by applying a linear filter technique and an efficient four-dimensional (4D) path integration (PI) procedure is applied in order to calculate the response statistics. The long-term analysis of nonlinear roll motion in random seas that takes into considerations of the response statistics obtained by the 4D PI method as well as the variation of the sea states could be a valuable reference for ship stability research.