Study On The Nonlinear Random Dynamic Behaviors Of Ship Roll

Lots of possessions and lives are lost when ship capsize. People pay more and more attention to study the ship accidents, especially the stability against capsizing. Capsizing is a very complicated event and the main difficulties involve two sides. One is the strong nonlinearity because of the large toss of ship. However, there are not enough effective methods to solve the strong nonlinear problems. The other is that the capsizing occurs in a probability because of the random characteristic of the waves force. As for the water on deck ship, it is harder to investigate the capsizing for its complicated behaviors. Now, only some experiential criteria are presented to prevent capsizing. Nevertheless, the shortcomings of them are revealed distinctly after a great deal of ships capsized that satisfied the current static criteria.The nonlinear dynamics for ship roll excited by the regular waves and random waves are studied by the nonlinear stochastic dynamic theory without and with considering the water on deck. The bifurcation and chaos related to capsizing are investigated, the capsizing mechanisms are farther interpreted, and the criteria for predicting ship capsizing are established. The calculation results are given for 66.01 meters long trawler.The main conclusions obtained are as following:(1) The stability for ship roll in regular waves is studied by the nonlinear dynamic methods without and with considering water on deck, respectively. The stable conditions for the periodic stationary roll motion are ascertained, and the jump phenomena are explained analytically. It is found that if water on deck doesn't occur, the stability of ship roll loses because of the large roll angle. After water on deck occurs, stability of ship roll loses under weak wave excitation, the roll response includes three equilibrium points and the center around which the ship rolls is transferred frequently and reiteratively, that may result in roll stability losing and ship capsizing if the ship is excited by some uncertain force.(2) The random chaotic parameter region of the ship roll without and with water on deck in the random waves is studied by the random Melnikov mean square criterion. It is found that water on deck affects ship stability severely. The area of the random chaotic parameter region relates closely with the wave excitation parameters, it increases with the increasing of the wave excitation. The area of the nochaotic parameter region diminishes greatly after water on deck occurs. The random chaos in the ship roll can be controled by increasing the damping, the stability against capsizing can be increased by improving ship exterior and adding the keel.(3) The calculational methods for the phase space flux of the ship roll are presented with considering water on deck in the random waves. The stability against capsizing is compared quantitatively by the phase space flux between the ship without condiering the water on deck and with considering the water on deck in the random waves. It is found that the water on deck affects ship's stability severely.(4) The probability density function of the ship roll without water on deck is calculated by the path integral method. It is found that the joint probability density function has a single peak. In the nochaotic parameter region, the shape of it goes to steady, and the ship roll is safe in probability 1. While in the chaotic parameter region, the value of the joint probability density function disappeared gradually, the probability of the ship holding in the safe states decreases as time progresses and it decreases more quickly for the strong wave excitation. The roll response will leave the safe states for enough time and the ship will capsize theoretically in the end. In the chaotic parameter region, the phase flux of the ship roll leaves the safe states periodically from neighborhood of the positive and the negative stability vanish angle. It is shown that the ship capsizing may relate to the roll angle exceeding the stability vanish angle when water on deck doesn't occur.(5) The probability density function of the ship roll with water on deck is calculated by the path integral method. It is found that the joint probability density function has two peaks and the ship roll process has two possible roll states. If the two peaks are unconnected, only one roll state can be achieved and no jump happened in the roll response for a set of intitial conditions of the phase plane. If the two peaks are connected, the roll response includes three equilibrium points and roll process jumps randomly from one roll state to another one. That may lead the ship to instability and even to capsizing. It is shown in Poincare maps that the random noise diffuses the area of the chaotic attractor of roll response.(6) The capsizing criteria of ship roll in the random seas are established based on the nonlinear random dynamic theory and the calculation process is modularized. This makes it easy to use the criteria in the real engineering.